Four variable-exponent taper equations and their modified forms were evaluated for lodgepole pine (Pinus contorta var. latifolia Engelm.) trees in Alberta, Canada. A nonlinear mixed-effects modeling approach was applied to account for within-and between-tree variations in stem form. Even though a direct modeling of within-tree autocorrelation by a variance-covariance structure failed to achieve convergence, most of the autocorrelation was accounted for when random-effects parameters were included in the models. Using an independent data set, the best taper equation with two random-effects parameters was chosen based on its ability to predict diameter inside bark, whole tree volume, and sectioned log volume. Diameter measurements from various stem locations were evaluated for tree-specific calibrations by predicting random-effects parameters using an approximate Bayesian estimator. It was found that an upper stem diameter at 5.3 m above ground was best suited for calibrating treespecific predictions of diameter inside bark, whole tree volume, and sectioned log volume.

A height-diameter mixed-effects model was developed for loblolly pine (Pinus taeda L.) plantations in the southeastern US. Data were obtained from a region-wide thinning study established by the Loblolly Pine Growth and Yield Research Cooperative at Virginia Tech. The height-diameter model was based on an allometric function, which was linearized to include both fixed-and random-effects parameters. A test of regionalspecific fixed-effects parameters indicated that separate equations were needed to estimate total tree heights in the Piedmont and Coastal Plain physiographic regions. The effect of sample size on the ability to estimate random-effects parameters in a new plot was analyzed. For both regions, an increase in the number of sample trees decreased the bias when the equation was applied to independent data. This investigation showed that the use of a calibrated response using one sample tree per plot makes the inclusion of additional predictor variables (e.g., stand density) unnecessary. A numerical example demonstrates the methodology used to predict random effects parameters, and thus, to estimate plot specific height-diameter relationships.

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Based on a multilevel nonlinear mixed model approach, a basal area increment model was developed for individual aspen ( Populus tremuloides Michx.) trees growing in boreal mixedwood stands in Alberta. Various stand and tree characteristics were evaluated for their contributions to model improvement. Total stand basal area, basal area of larger trees, and the ratio of target tree height to maximum stand height were found to be significant predictors. When random effects were modeled at the plot level alone, correlations among normalized residuals remained significant. These correlations were successfully removed when random effects were modeled at both plot and tree levels. The predictive abilities of two alternative models were evaluated at the population, plot, and tree levels. At the tree level, a tree measured at the first growth period was used for estimating random parameters, and basal area increments of that tree in future growth periods were subsequently predicted. At the plot level, one to five trees in each plot at each growth period were used to estimate random parameters. Basal area increments of the remaining trees in the same plot at the same growth period were subsequently predicted. The final model provided accurate predictions at all three levels.

SUMMARYIn this study, two different approaches for modeling the height-diameter relationship were analyzed. Data were obtained from 3,492 sample plots established in 105 operational pre-harvest inventories in the province of Arauco, VIII Region. Measures of precision and bias permitted to evaluate and compare equations within and between modeling approaches. Moreover, a comparative analysis to determine the effect of total tree height prediction in stand volume and multi-product calculation was also investigated. The 2-parameter local equations were more precise and stable in terms of convergence than 3-parameter equations. Measures of precision and bias showed that generalized equations performed better than local equations. Paired t tests (α = 0.05) detected significant differences in total and merchantable volume estimates when applying a local or generalized equation. Contrarily, two of the three log products showed no significant difference.Key words: height-diameter relationship, total height, radiata pine. RESUMENEsta investigación analizó dos tipos de estrategias de modelamiento de la relación altura-diámetro (h/d) para ser utilizadas en labores de inventario. La información requerida se obtuvo de 3.492 parcelas temporales establecidas en 105 rodales de precosecha en la provincia de Arauco, VIII Región. El análisis consistió en una evaluación y comparación dentro y entre estrategias de modelamiento en base a medidas de precision y sesgo. Adicionalmente, se cuantificó el efecto en la estimación de alturas totales sobre la predicción de volúmenes y productos. Las ecuaciones locales con 2-parámetros fueron más precisas y estables en términos de convergencia en comparación a ecuaciones con 3-parámetros. En todas las evaluaciones realizadas las ecuaciones generalizadas presentaron mejores valores de precisión y sesgo que las ecuaciones locales. La aplicación de una prueba t para observaciones pareadas (α = 0,05) detectó diferencias significativas en la predicción de volúmenes totales y comerciales al utilizar ecuaciones locales o generalizadas. Sin embargo, dos de tres productos considerados no indicaron diferencias significativas.Palabras clave: relación altura-diámetro, altura total, pino radiata.

Background: Over the last decades interest has grown on how climate change impacts forest resources. However, one of the main constraints is that meteorological stations are riddled with missing climatic data. This study compared five approaches for estimating monthly precipitation records: inverse distance weighting (IDW), a modification of IDW that includes elevation differences between target and neighboring stations (IDW m), correlation coefficient weighting (CCW), multiple linear regression (MLR) and artificial neural networks (ANN). Methods: A complete series of monthly precipitation records (1995-2012) from twenty meteorological stations located in central Chile were used. Two target stations were selected and their neighboring stations, located within a radius of 25 km (3 stations) and 50 km (9 stations), were identified. Cross-validation was used for evaluating the accuracy of the estimation approaches. The performance and predictive capability of the approaches were evaluated using the ratio of the root mean square error to the standard deviation of measured data (RSR), the percent bias (PBIAS), and the Nash-Sutcliffe efficiency (NSE). For testing the main and interactive effects of the radius of influence and estimation approaches, a two-level factorial design considering the target station as the blocking factor was used. Results: ANN and MLR showed the best statistics for all the stations and radius of influence. However, these approaches were not significantly different with IDW m. Inclusion of elevation differences into IDW significantly improved IDW m estimates. In terms of precision, similar estimates were obtained when applying ANN, MLR or IDW m , and the radius of influence had a significant influence on their estimates, we conclude that estimates based on nine neighboring stations located within a radius of 50 km are needed for completing missing monthly precipitation data in regions with complex topography. Conclusions: It is concluded that approaches based on ANN, MLR and IDW m had the best performance in two sectors located in south-central Chile with a complex topography. A radius of influence of 50 km (9 neighboring stations) is recommended for completing monthly precipitation data.

Population-averaged (PA) and subject-specific (SS) approaches for modeling the height of dominant or codominant lodgepole pine ( Pinus contorta Dougl. ex Loud.) trees were evaluated using six candidate models derived from the Chapman–Richards and logistic functions. The true PA response obtained from separate fits of the models was compared with the typical mean (TM) response computed using only the fixed-effects parameters of the mixed-effects models. Results showed that the TM response had higher prediction errors than the PA response, suggesting that a true PA response and not the TM response is needed to reflect the overall mean response of the model. The SS approach produced improved height predictions relative to the PA approach when evaluated using independent validation data. In addition, the logistic performed better than the Chapman–Richards function, regardless of whether the SS or PA approach was applied. Among the candidate models, the logistic function with the inclusion of site index gave the most accurate predictions. Three scenarios of calibrating the mixed-effects models on the validation data set were compared. The SS predictions obtained using only one premeasured observation per subject were poorer than those using all observations, but they were still generally better than PA predictions.

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