The quantity x is proportional to the average loading on the site of 1/4- to 1-inch fuel 

 pieces. When only pines are present in the fuel bed, or when none are present, this 

 formula provides a prediction of fuel bed depth for fire modeling. But when both types 

 are present, the mixed species fuel bed depth will contain contributions for both types. 

 The model for mixed type fuel bed depths used in the HAZARD model is as follows: 



Let Xj = expected 1/4- to 1-intercept count per foot for pine types, 

 and x 2 = expected 1/4- to 1-intercept count per foot for other types. 



If the two types are randomly distributed over the site, then the fraction of the total 

 1/4- to 1-inch size class loading that is pine type should be (ignoring particle density 

 differences) f x , where 



f l = Xi/(x 1 + x 2 ) 

 and the fraction for other types is f 2 , where 



f2 = x 2 /(x 1 + x 2 ) = 1 - f 



Now, if the two types were segregated on the site, so that a fraction fi of the 

 site area would be covered by pine species and f 2 by others, the expected intercept 

 count in the pine-covered area would be xi/fi and the bulk depth in the pine-covered 

 area would be 



6 (1) = a ZxT/fT. 

 o l' i 



Similarly, the bulk depth of the other fraction of the area would be 



(2) 



6 = VW 



On such a segregated site, the average bulk depth would be 6 , where 



6 = f x 5 (l) + f 2 6 (2) . 

 1 o z o 



We take this latter expression to be the average fuel bed depth for the mixed type sit- 

 uation. This equation can be rewritten by substituting for the f and 6 q values to give 



6 q = (a]^ + a 2 x 2 )//x 1 + x 2 . 



Other factors that affect initial fuel bed depth are reflected in this formula by chang- 

 ing the values of aj and a 2 in accordance with the results discussed earlier (fig. 4) . 



Foliage Loss and Settling 



The early effects of aging on debris fuels are settling of the fuel bed and loss of 

 foliage and fine twigs to the forest floor. For modeling fire behavior in slash, it is 

 necessary to quantify rate of settling and the loss of foliage and fine twigs. To 

 operate the HAZARD model, data from Olson and Fahnestock (1955), Fahnestock and Dieterich 

 (1962), Steele (1960), Wagener and Offord (1972), and Brown (1970a) were integrated to 

 describe loss of material (fig. 10). Not all foliage that drops from the branches was 

 excluded from the fuel complex because some foliage remaining in the litter layer and 

 suspended as mats in the slash is still available as fuel for a surface fire. 



Settling of slash was modeled as a reduction in depth using table 3, Fahnestock 

 and Dieterich (1962), and Kiil (1968). This study, together with others cited, permitted 

 construction of a settling model adequate for hazard appraisal (fig. 11) . 



18 



