A parameter recovery model for estimating black spruce diameter distributions within the context of a stand density management diagram

Abstract

The objectives of this study were to develop and subsequently demonstrate a parameter prediction approach for estimating black spruce (Picea mariana (Mill. ) BSP) diameter frequency distributions within the context of a stand density management diagram (SDMD). The approach consisted of three sequential steps: (1) obtaining maximum likelihood estimates for the location, scale and shape parameters of the Weibull probability density function for 153 empirical diameter frequency distributions; (2) developing and evaluating parameter prediction equations in which the Weibull parameter estimates were expressed as functions of stand-level variables based on step-wise regression and seemingly unrelated regression techniques; and (3) explicitly incorporating the parameter prediction equations into the SDMD modelling framework. The results indicated that the Weibull function was successful in characterizing the diameter distributions within the sample stands: the fitted distributions exhibited no significant (p ≤ 0. 05) differences in relation to their corresponding observed distributions, based on the Kolmogorov-Smirnov test. The parameter prediction equations described 94, 94 and 89% of the variation in the location, scale and shape parameter estimates, respectively. Furthermore, evaluation of the recovered distributions in terms of prediction error indicated minimal biases and acceptable accuracy. As demonstrated, incorporating the parameter prediction equations into an algorithmic version of the SDMD enabled the prediction of the temporal dynamics of the diameter frequency distribution by initial density regime and site quality. Additionally, an executable version of the resultant algorithm with instructions on acquiring it via the Internet is provided. Key words: 3-parameter Weibull probability density function, stepwise and seemingly unrelated regression, predictive error, product value, algorithm, Internet