SENSITIVITY ANALYSIS 



The functional forms derived above are admittedly complicated, but the evaluation 

 of such expressions is relatively easy with the aid of modern digital computers. These 

 equations were programed and evaluated on both the EC-1020 computer at the Leningrad 

 Forestry Research Institute and the CDC-7600 at the Lawrence Berkeley Laboratory's 

 computer facility on the campus of the University of California at Berkeley. 



The results of these computations are displayed in tables 2. and 3. Table 2 gives 

 values of the area burned divided by the area of the fire at the time suppression begins. 

 Table 3 gives values of the time required to contain the fire (At) , multiplied by the 

 rate of suppression (X), and divided by the perimeter of the fire at the time 

 suppression starts. Since the product X At is numerically equal to the length of 

 perimeter of the burned area, the values in table 3 are also equal to the ratios of 

 final perimeters to initial perimeters. 



In terms of area burned (table 2) we can conclude that the tactic of suppressing 

 the head fire first (tactic 2) is significantly superior (>50 percent) to suppressing 

 the backing fire first only when the head fire spreads at approximately 3 times the rate 

 of the backing fire and the rate of suppression is no more than 3 times the forward 

 rate of spread. For rates of suppression 5 times the head fire rate of spread or 

 greater, neither fire shape nor tactics alter the burned area substantially. For fires 

 which show little directional difference in spread rate (Vp/V^ <3) the choice of 

 tactics is of little consequence unless X^ ^^^p" 



The sensitivity of the burned area to the ratio of suppression rate to forward rate 

 of spread (X/Vp) is less in the case of tactic 2 than in the case of tactic 1, for 

 fixed fire shape parameters (V^/Vp , Vg/V^,n) . Conversely, the sensitivity of the 

 burned area to fire shape parameters for fixed values of X/V is much greater for tactic 

 2 than for tactic 1, but in either case the sensitivity to tne value of n is less than 

 the sensitivity to V^/Vp. The latter parameter becomes increasingly important as 

 X/Vp approaches one, for both tactics. 



The statements made above also apply to the time required for containment (table 3). 



In general, the time required for containment varies less than does the burned area, 



no matter which variable is considered. Significant differences (>50 percent) between 



tactics appear only for fires for which the forward spread rate much exceeds the flanking 



rate (V^/V <0.4), except for the case when fire suppression is almost impossible 

 1 r 



(X/Vp = 1.5). As in the case of burned area, the containment time is more sensitive to 

 fire shape under tactic 2 than under tactic 1, but the converse is true for sensitivity 

 to suppression rate for fixed fire shape. 



It should be stressed that the area and perimeter ratios given in tables 2 and 3 

 are to their values at the time suppression begins. In order to establish the values of 

 burned area and containment time, these numbers must be multiplied by initial area 

 (table 2) or by the ratio of initial perimeter length to rate of suppression (table 3). 

 Because of this fact, one can conclude that the sensitivity of actual burned area to 

 initial fire size (r ^(O) used to normalize entries in table 1) is simply magnified 

 by the factors in taSle 2. 



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