USDA Forest Service

Pacific Southwest Research Station

Pacific Southwest
Research Station

800 Buchanan Street
Albany, CA 94710-0011
(510) 883-8830
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Publications and Products

Title: Improved equations for the density management diagram isolines of ponderosa pine stands

Authors: Jang, Woongsoon; Ritchie, Martin; Zhang, Jianwei

Date: 2020

Source Forest Science. 67(1): 93-102.


This study was conducted to improve estimation of concomitant variables for implementation of a stand density management diagram (SDMD) for ponderosa pine (Pinus ponderosa Laws.) in northern California and Oregon. In traditional SDMD, isolines for variables such as stand volume are presented in such a way that uncertainty with estimation is not available. We developed the new top height and stand volume equations, as well as aboveground biomass and percent canopy cover, for building isolines in the SDMD using high-quality data collected from well-managed even-aged stands. The data were selected from the USDA Forest Service’s Pacific Southwest Research Station database. A total of 829 observations (from 113 plots across 15 sites in Oregon and California) were used for model construction. In addition, covariance-variance structures of all of the estimated parameters were provided so that users can evaluate the uncertainty associated with predictions. The model validation results indicated that the predictions made from fixed-effects model forms performed better than the current volume equation of SDMD, as well as those from mixed-effects model forms using the population average effect. The proposed equations provide enhanced predictions and additional useful information about managed ponderosa pine stands, including their uncertainty.

Keywords: stand density management, silviculture, stocking diagram, mixed-effects model, fixed-effects model

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    Jang, Woongsoon; Ritchie, Martin W; Zhang, Jianwei. 2020. Improved equations for the density management diagram isolines of ponderosa pine stands. Forest Science. 67(1): 93-102.
Last Modified: February 24, 2021