This equation is for both blackjack and yellow pine. Insufficient data precluded separate 

 equations. 



TOTAL STEM CUBIC-FOOT VOLUME EQUATIONS 



Existing equations or data for developing new equations to predict total stem cubic foot 

 volume in 1-inch diameter classes were not available for northern Arizona. As an alternative, 

 I used tree volume equations developed by Hann and Bare (1978) for yellow and blackjack pine 

 on the Coconino National Forest of northern Arizona. While application of an individual tree 

 volume equation to diameter class attributes could produce biased volume estimates, 1 felt the 

 smallness of 1-inch classes would minimize the potential problem. 



Structure of Simulator 



The four models --upgrowth, mortality, conversion from blackjack pine to yellow pine, and 

 ingrowth--interact in the following fashion: 



1. Present number of trees in each diameter and vigor class provide the starting point. 



2. Mortality is computed and subtracted from each class to give the number of trees 

 expected to survive to the end of the growth period. 



3. Using diameter class growth of the survivors and the appropriate within diameter 

 class distribution, the number of trees moving to various diameter classes is determined. 



4. At the start of each fourth growth period, the blackjack-to-yellow pine conversion 

 rates for survivors are calculated; otherwise, the conversion rates are set to zero. The 

 conversion rates and upgrowth information then are used to allocate the survivors to the 

 appropriate "future" diameter and vigor classes. 



5. Ingrowth for the next 5-year period is computed and added to the 4- and 5-inch classes. 



6. Removals due to cutting are made from each diameter class. Cutting, therefore, 

 presumably occurs at the end of the growth period. This step completes the "future" diameter 

 distribution . 



7. This distribution then becomes the present diameter distribution, and the cycle 

 starts again. A system interaction chart is found in figure 8. 



VALIDATION OF SIMULATOR 



The problem of validating a simulator has troubled modelers for years. Shannon (1975) 

 identified and described the philosophies of three approaches. "Rationalism holds that a 

 model is simply a system of logical deductions from a set of premises, which may or may not be 

 open to empirical verification or appeal to objective experience" (page 212) . "Empiricism 

 refuses to admit any premises or assumptions that cannot be verified independently by experi- 

 ment or analysis of empirical data" (page 214). Finally, absolute pragmatism holds that a 

 model is designed to meet a need, and if the model succeeds in meeting the need, then it has 

 been validated. 



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