Improved Equations for the Density Management Diagram Isolines of Ponderosa Pine Stands

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. Study Implications: Existing stand density management diagrams often present isolines for estimation of volume and dominant height, but these lack sufficient information for estimation of uncertainty associated with these estimates. Here, using data from research plots within even-aged stands in northern California and central Oregon, we present models with estimates of uncertainty for volume, dominant height, biomass, and percent canopy cover. The use of these is illustrated with the standview package in R. The benefit of this approach is that the isolines are actually not needed any longer, as the estimates and their associated uncertainty can be derived for any observed values with the functions provided with no need to eyeball a volume or other estimate from isolines.

Automated summary

This study aimed to improve estimation of concomitant variables for ponderosa pine stands in northern California and Oregon by developing new equations for building isolines in the stand density management diagram. Using high-quality data, the model validation results showed that predictions from fixed-effects model forms performed better than existing volume equations of SDMD. The proposed equations provide enhanced predictions and additional useful information about managed ponderosa pine stands, including their uncertainty.