Compatible whole-stand and diameter distribution models for loblolly pine plantations

A method was developed to approximate the diameter distribution of unthinned plantations of loblolly pine from whole stand predictions of stand attributes. The beta probability density function (pdf) and the Weibull pdf were used as models for the diameter distribution function for estimating a stand attribute (such as average diameter at breast height (dbh) or total volume per acre) and the whole stand estimation of the attribute was defined. The given estimates of k stand attributes from whole stand models, the k parameter of the pdf were estimated (recovered).

Two types of parameter recovery models were constructed. The first used equations for the non-central moments of dbh. For the beta pdf, equations for the predicted first moment (average dbh) and second moment (basal area per acre/(0.005454 N)) were used to compute the analytic solution for parameter α and β. The endpoints of the pdf were defined to be the predicted minimum dbh minus 0. 6 inches and maximum dbh plus 0.6. In the case of the Weibull pdf, the parameter c was solved from the coefficient of variation which itself was computed from the predicted first and second non-central moments. Then given this value of c, b was solved for using the predicted average dbh. The parameter a was set equal to one-half predicted minimum dbh.

The second type of parameter recovery model used volume as one of the stand attributes used to solve for the parameters. Due to failure of the numerical solution algorithms to consistently converge to a solution for the parameters, the beta pdf could not be used. For the Weibull though solutions were always possible. The parameters a and c were estimated as before and b was then solved using the diameter distribution yield equation for total volume per acre.

The three models described above achieved a solution for the parameters 100% of the time. Comparison of the three using Kolmogorov-Smirnov statistics showed all three to be nearly equal in their ability to approximate the diameter distribution of stands. When compared to other conventional diameter distribution prediction methods (Burkhart and Strub 1974 and Smalley and Bailey 1974a), the parameter recovery models proved as good as or better than these other methods.

In unthinned loblolly pine plantations the parameter recovery models proved to be a feasible alternative for predicting diameter distributions. The major advantage of the models is the numerical compatibility of the whole stand estimates of stand attributes and the diameter distribution estimates. Thus given whole stand estimates, such as basal area per acre or total cubic-foot volume per acre, the distribution of these attributes by diameter classes can be obtained.