Observations for Risk Management

What Do We Need To Know To Model Fire?

Ignition Rate

Fire ignitions are typically caused by the overturning and breakage of building contents (i.e., ignitions due to open flame or chemical reactions), structural deflections resulting in damage and short-circuiting of electrical wiring, and ruptured gas lines. As such, there is a generally positive correlation between the number of ignitions and earthquake intensity.

The probability of an ignition per million square feet of commercial high rise is not the same as the probability of an ignition per million square feet of single family residential structures. Fire codes in commercial buildings are more stringent, sprinkler systems further reduce the risk, building materials are less flammable, etc.

Once the number of ignitions is generated, they are stochastically placed throughout the ZIP Code / Modeled area.

Fire spread

Once a fire has been ignited, the growth of this fire must be modeled.

The fire spread rate is a function of building density, building spacing, building plan area, the percentage of buildings that are fire resistant, and wind speed. Models yields a burn area as a function of time. Also depends on smallest geographic area model looks at. (i.e., Zip code vs. VRG)

Fire spread parameters are estimated for four different urban types: town/suburban, urban, commercial, dense commercial.

The spread rate is, in part a function of local wind speed, based on data of annual mean wind speed and variability.

This could lead to an underestimation of the tail of the Fire Following EP curve. Since in this one model, no direct Santa Ana input is present; peaks smoother over averages.

Fire Suppression

Finally, fire response and suppression is simulated. Most models incorporate distributions of fire discovery and report times that are based on historical data.

Report time generally increases as intensity increases, as a result of, among other things, interruptions in telephone service.

Each fire is probabilistically assigned a discovery and report time and an engine is assigned to the fire.

The time it takes for local authorities to respond is estimated as a function of the fire discovery and reporting time and fire engine speed. More intense earthquakes are more likely to render roads impassable, break water mains, or result in other events that affect suppression capability.

Fire Damage Estimation

Fire losses are computed for each fire by taking the burn area and multiplying by an estimate of construction cost per square foot of the affected construction class.

Total losses for each fire class in a ZIP Code are capped by the maximum exposure in that ZIP Code for that fire class.

RMS Industry Loss Curves
EQ Shake Only And EQ Shake and Fire Following Combined
California, All Lines of Business - No Demand Surge
Gross Occurrence Loss Figures

Critical Prob.	Return Period	Shake and Fire	Shake Only	% Difference
10.00%	10	$2,524,162,949	$2,422,136,107	4%
4.00%	25	8,393,428,721	7,336,396,008	14%
2.00%	50	14,552,105,524	12,228,107,476	19%
1.00%	100	21,659,239,895	17,760,814,489	22%
0.40%	250	32,387,467,829	25,886,614,205	25%
0.20%	500	41,141,109,523	32,277,032,623	27%
0.10%	1,000	49,941,440,520	38,327,605,263	30%
0.01%	10,000	77,925,226,910	56,960,351,104	37%
Average Annual Loss		$1,216,873,535	$1,054,679,430	15%
Standard Deviation		4,523,737,653	3,665,905,471	23%
Pure Premium Fire Differential		$162,194,105
As % of Shake Loss		15%

RMS Industry Loss Curves
EQ Shake Only And EQ Shake and Fire Following Combined
All US, All Lines of Business - No Demand Surge
Gross Occurrence Loss Figures

Critical Prob.	Return Period	Shake and Fire	Shake Only	% Difference
10.00%	10	$4,053,431,984	$3,747,739,088	8%
4.00%	25	11,046,523,287	9,466,958,935	17%
2.00%	50	18,164,251,611	15,171,797,581	20%
1.00%	100	27,484,510,919	22,323,228,645	23%
0.40%	250	43,535,975,556	35,064,605,755	24%
0.20%	500	59,197,064,588	48,073,044,639	23%
0.10%	1,000	79,011,932,016	67,813,207,519	17%
0.01%	10,000	138,325,250,820	121,727,085,426	14%
Pure Premium		$1,838,982,887	$1,608,939,863	14%
Standard Deviation		6,503,531,425	5,474,202,264	19%
Pure Premium Fire Differential			$230,043,024
As % of Shake Loss			14%

Conclusion

Fire Following is a real exposure, if difficult to quantify.

The 2003 Brushfires were not fire following losses, but the magnitude of that season's loss illustrated the potential for loss in an earthquake during a Santa Ana season.