Stem Taper Models For Dahurian Larch,Korean Spruce,and Manchurian Fir In Xiaoxing’an Mountains,Northeast China

Stem taper models are an essential component of growth and yield modelling.These models supersede the volume tables as they can estimate upper stem diameter,merchantable height to any diameter above ground,the merchantable and total stem volume.Furthermore,taper models are useful in timber quality studies and modelling of carbon allocation in different stem sections.They are also instrumental in assessing the impact of silvicultural treatments on stem taper.Dahurian larch(Larix gmelinii Rupr.),Manchurian fir(Abies nephrolepis Maxim),and Korean spruce(Picea koraiensis Nakai)are important conifer species of economic and ecological significance.Stem taper models are required for the sustainable management of these species.Stem taper models are valuable tools to provide the stem profile and predict total and merchantable volumes.The aim of this study was to present stem taper models for Dahurian larch,Manchurian fir,and Korean spruce and investigate further the impact of adding different crown variables regarding improvement in estimating diameter and volume.The study was carried out in two phases.Initially,eight well-known taper models were evaluated with a dataset of 188 destructively sampled trees of Manchurian fir and Korean spruce.These models represented four segmented taper models,i.e.Max and Burkhart(1976),Clark et al.(1991),and Fang et al.(2000),and four variable form taper models,i.e.Bi(2000),Lee et al.(2003),Kozak(2004)and Sharma and Parton(2009).The dataset comprised of 3570 diameter and height measurements was used to fit the models with generalized non-linear least squares method.A firstorder continuous-time error structure was used for the adjustment of autocorrelation.The model of Clark et al.(1991)delivered the best predictions of diameter,total volume,and merchantable volume whether the diameter measurements at 5.3 m was available or attained through prediction.The models of Kozak(2004),Max and Burkhart(1976),Fang et al.(2000),and Bi(2000)were among the good performers depending upon the variables and species.In the second phase,the top model of Clark et al.(1991)and other good performers were independently fitted with height and diameter datasets of 473 trees of Dahurian larch,Korean spruce,and Manchurian fir.The datasets were randomly split into two sets for each species: 80%of total data(379 trees)for model fitting and 20% of total data(94 trees)for model validation.A third-order continuous-time error structure was incorporated to adjust the autocorrelation in the data.The condition number was used to detect multicollinearity in the models.The performance of the models was evaluated using statistical analysis and graphical interpretation of diameter and volume residuals against relative heights and diameter classes.The model of Clark et al.(1991)best predicted the stem profile,total volume,and merchantable volume,whether the diameter measurement at 5.3 m was available or obtained through prediction.After selecting the leading model of Clark et al.(1991),it was refitted as a nonlinear mixed-effects model.This study also suggested that Clark et al.’s(1991)model(fixed-effects)delivered better diameter estimates than Kozak’s(2004)model that was calibrated for diameter measurements at 5.3 m using validation data.The calibrated Kozak(2004)model increased the values of RMSE by 3–8% and MAB by 8–11% depending on the species.In the later part of the second phase,the most consistent model form of Clark et al.(1991)was fitted to 276 trees of Dahurian larch,Korean spruce,and Manchurian fir from the same data containing crown information.This step aimed to examine the effects of adding several crown variables to the model of Clark et al.(1991)in increasing the prediction accuracy of stem profile and volume of the species under study.Although several taper studies have accounted for crown architecture,the previous research has generally concentrated on limited crown variables.The crown variables used in this study comprised crown width(CW),crown length(CL),crown ratio(CR),crown shape(CS),diameter at the crown base(CD),and height to live crown base(HCB).A third-order continuous-time error structure was incorporated for the adjustment of autocorrelation.Model fitting was achieved in two steps by using the NLMIXED procedure and the MODEL procedure of SAS,respectively.The original and adapted models were evaluated with fit statistics and graphical interpretations.The inclusion of crown variables marginally decreased the RMSEs for all the species.The plots of RMSE reflected that the adapted models slightly improved the predictions of diameter and volume for the upper stem sections(>50–90%)of the species.The study showed that crown variables affect the stem taper,however,the original model of Clark et al.(1991)practically captured that affect.