Fuel bed depth was related to the expected number of intercepts of 1/4- to 1-inch- 

 diameter fuel particles per foot of planar intersect by fitting regressions through 

 aggregated data points. The 1/4- to 1-inch particles served as a proxy for the loading 

 of debris fuel under 3 inches in diameter. The fitting of data points resulted from a 

 three-step averaging process as described below: 



1. For each study area, the data from the two transects were treated as a single 

 set. Only sample points at which intercepts were counted were assembled in the data 

 set, so the "unit" of sample information consisted of a triplet of numbers--the bulk 

 depth, in inches; the total numbers of intercepts of 1/4- to 1-inch size class fuels in 

 the two crossed sample planes; and the number of intercepts of 1- to 3-inch size class 

 fuels in the same two (extended) planes. 



For inspecting these triplets of numbers, they were aggregated and displayed in 

 five categories, according to the number of 1/4- to 1-inch intercepts: 0-2, 3-6, 7-13, 

 14-22, and 23 or more intercepts. The display (table 1) consisted of the following 

 descriptors for each subset: 



a. Average bulk depth 



b. Average 1/4- to 1-inch intercept count 



c. Number of sample triplets in the subset 



d. Mean square bulk depth 



e. Mean square 1/4- to 1-inch intercept count. 



Scrutiny of such tables quickly revealed sample points that were obviously not rep- 

 resentative, so they could be culled from the data set. The mean square depth figures 

 served well to permit the "outlaw" points to be identified. Fewer than 10 points were 

 discarded from more than 1,500 collected. 



2. These data were analyzed in many ways in attempting to discover trends and 

 correlations. One fact that soon became evident was that no substantial dependence of 

 bulk depth on the 1- to 3-intercept count could be established, whether or not the 1/4- 

 to 1 -intercept count was included. This allowed further simplification by combining 

 data for all 1- to 3-intercept counts. Table 2 displays this simplified data aggrega- 

 tion. An asterisk indicates that a sample point has been discarded in computing the 

 averages shown and two asterisks indicate the discarding of two data points. These data 

 form the basis for the regression relationships between bulk depth and number of 1/4- to 

 1-inch intercepts. 



3. Data in table 2 were grouped by combinations of skidding method, species, and 

 age of slash. Constrained regressions were applied to the data because logically if no 

 1/4- to 1-inch fuel particles exist there should be no bulk depth. Analysis using un- 

 constrained regressions supported this approach in that the constant terms were small 

 and often statistically nonsignificant. 



In deriving the regression equations, the data from all units aggregated were 

 averaged. That is, all the bulk depth-intercept count pairs in the intercept count 

 range 0-2 were averaged, all those in the range 3-6 were averaged, etc. Then the re- 

 gressions were formed by weighting each resultant aggregate data point by the number 

 of its supporting measurements. 



Scatter diagrams of these "grand average" points showed a fraction power law form, 

 so we chose to regress the average bulk depth against the square root of the average 

 number of 1/4- to 1-inch intercepts. 



5 



