APPENDIX A:
ANALYTICAL SUMMARY OF THE PROCEDURES USED IN STAND GENERATION

        The primary purpose of the stand generator is to convert some very 
broad stand descriptors of even-aged mixed species stands into a one acre re-
presentation of a plausible tree by tree inventory.  The initial input by 
species is:
                a) fifty year breast high age base site index
                b) average breast high age of dominants
                c) stems per acre
                d) quadratic mean DBH (optional)
                e) record count (optional)
From this information, a tree list is generated where each record has the 
following characteristics.
                a) species indicator code
                b) DBH
                c) total height
                d) live crown ratio
                e) per acre weight

A.  Site-Age Adjustments
        Initially, the site index and age of either redwood or Douglas-fir 
must be specified.  One of these species, which must have site index and age 
supplied, is designated as a control species.  If a tree per acre value great-
er than 25 is supplied for any species and the site index and/or breast height 
age is not supplied they will be estimated by the program (Krumland and 
Wensel, 1979a). 

B.  Diameter Distribution Estimates
        Site index, age, and stems per acre by species are all that is required 
to estimate parameters in the diameter distribution models (Krumland and 
Wensel, 1979a).  If the quadratic mean DBH is not supplied for any species 
group, Model I will be used.  Otherwise, Model II  will be utilized.
        In cumulative form, the diameter distribution model is
                F(di ) = 1-exp[-((di-a)/b)c]
where F(di )  = Percentage of trees between "a" and "di" inches DBH for a 
                particular species.

      a,b,c,  = Species Specific Model parameters with "a" being ther minimum  
                DBH.
        From this expression the percentage of trees between di and dj inches 
        (dj  > di) can be computed as 
                exp [-((di-a)/b)c] - exp [-((dj-a)/b)c]

C.  Record Generation
        By program default, or user modification, the number of records (NR )
for a particular species is internally available in the program along with the number of trees per acre (TPA) .  Tree diameters are generated for each of the NR records by dividing the range of diameters into NR equal intervals.  For each tree diameter a weight, wi, is computed to represent the number of trees per acre represented by tree 'i' with DBH1, where   àà·wi = TPA.
        The process is illustrated as follows:
1)      As the upper limit of the Weibull distribution is infinity, a finite 
range ( DMIN - DMAX) is established as the diameters corresponding to the 
cumulative probabilities of 2 and 99.5 percent respectively.  These DBH limits 
are estimated as
                DMAX = a+b (-log [0.005] )1/c
                DMIN  = a+b (-log [0.98] )1/c
        The asymmetry of the range maintains approximately the same average 
stand quadratic mean diameter after record generation
2)      The constant DC is computed as
                DC = [DMAX - DMIN]/NR
3)      For any species tree record i (i=1,NR), the DBH assigned is
                DBHi = DMIN + (i) DC - DC/2
4)      The per acre weight assigned to the ith species record is       
        wi = {F(a+(i)DC) - F(a+(i-1)DC)}(TPA)(1/0.975)
5)      Average DBH of the trees in the top 20% of the diameter distribution 
for a species (Dm) is obtained by numerically integrating the estimated dia-
meter distribution model.
6)      Using Dm, assigned DBH's, average height of dominants estimated by 
site index curves, and the models presented in Research Notes 8 and 12 
(Krumland and Wensel, 1978 and 1979b), total heights are then assigned to 
each record.
7)      The ad-hoc procedure given by Krumland and Wensel (1981) is used to 
estimate crown ratios.

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