Evaluation of Weibull-based parameter prediction equation systems for black spruce and jack pine stand types within the context of developing structural stand density management diagrams

Abstract

The objective of this study was to evaluate the predictive ability of Weibull-based parameter prediction equation (PPE) systems developed for natural (density unregulated) and managed (density regulated) black spruce (Picea mariana (Mill.) BSP) and jack pine (Pinus banksiana Lamb.) stand types (n = 6), using (1) seemingly unrelated regression (SUR) employing a recursive system specification, (2) cumulative density function regression (CDFR) in which the location parameter was estimated indirectly employing a minimum diameter function (denoted CDFR(1)), and (3) CDFR in which the location parameter was estimated directly from stand-level variables (denoted CDFR(2)). An Ontario-based calibration data set consisting of diameter frequency distributions and associated stand-level variables derived from 1591 permanent sample plot (PSP) measurements was used to develop SUR-based, CDFR(1)-based, and CDFR(2)-based PPE systems. The calibration data set and an Ontario-based independent test data set, which consisted of stand-level variables and associated diameter frequency distributions derived from 244 PSP measurements, were used to evaluate the resultant PPE systems. Based on the approximate equivalency among the PPE systems in terms of (1) goodness-of-fit indices, (2) lack-of-fit statistics, (3) prediction error indices, and (4) stand-level product value prediction error, all three parameterization methods were found to be of equal utility, irrespective of stand type.