A generalized nonlinear mixed-effects height-diameter model for Eucalyptus globulus L. in northwestern Spain

A generalized height–diameter model was developed for Eucalyptus globulus Labill. stands in Galicia (northwestern Spain). The study involved a variety of pure stands ranging from even-aged to unevenaged. Data were obtained from permanent circular sample plots in which trees were sampled within different radii according to their diameter at breast height. A combination ofweighted regression, to take into account the unequal selection probabilities of such an inventory design, and mixed model techniques, to accommodate local random fluctuations in the height–diameter relationship, were applied to estimate fixed and random parameters for several models reported in the relevant literature. The models that provided the best results included dominant height and dominant diameter as fixed effects. These models explained more than 83% of the observed variability, with mean errors of less than 2.5 m. Random parameters for particular plots were estimated with different tree selection options. Height–diameter relationships tailored to individual plots can be obtained by calibration of the height measurements of the three smallest trees in a plot. An independent dataset was used to test the performance of themodel with data not used in the fitting process, and to demonstrate the advantages of calibrating the mixed-effects model

A Comparison of Model Forms for the Development of Height-Diameter Relationships in Even-Aged Stands

[EN] Several model forms were analyzed to develop a height-diameter (h-d) relationship for even-aged, birch-dominated stands (8,454 h-d pairs of 198 plot-inventory combinations) in northwestern Spain. A basic model (which includes only d as predictor) and a generalized model (which also considers stand variables as regressors) were selected from among available models. Fixed and mixed forms of these models were evaluated. An approximate Bayesian estimator was used to obtain a calibrated response (prediction with fixed parameters and random effects) of the mixed models from prior height measurements of trees selected by different strategies. From a practical point of view, the calibrated basic mixed model is recommended if a randomly selected sample of 4-11 trees is available or if only the 3 trees that are the diameter quartiles are measured. If the random sample includes more than 11 trees, the basic fixed model should be locally fitted, and the generalized fixed model is recommended when only dominant height is known. Finally, the predictions of the latter model may be outperformed by the calibrated generalized mixed model, which also requires inclusion of the height of the smaller diameter treesSIThis work was supported by the Spanish Ministry of Education and Science (AGL2007-66739-C02-01) and the European Regional Development Fun

Development of a stand density management diagram for radiata pine stands including assessment of stand stability

[EN] A stand density management diagram (SDMD) was constructed for Pinus radiata D. Don plantations in Galicia (north-western Spain) on the basis of four equations that were fitted simultaneously to data collected from 223 permanent plots. The relative spacing index was used to characterize the growing stock. The diagram provides information about quadratic mean diameter, stand merchantable volume, stand above-ground biomass, stand stem biomass and stand carbon pools. In addition, an estimation of the average slenderness coefficient for the whole stand and for each quarter of the stand diameter distribution was included. This information can be used to assess the stability of the whole stand and different crown classes, respectively. The SDMD outlined here allows foresters to make quick and easy comparisons among different thinning schedules in which both timber production and the risk of damage from wind or snow are considered. Two alternative density management systems, one that includes thinning operations and another that only includes the density-related mortality provided by a mortality function, are outlined in the diagramSISpanish Ministry of Education and Science (AGL2004- 07976-C02-01

Development of crown profile models for Pinus pinaster Ait. and Pinus sylvestris L. in northwestern Spain

[EN] We used data from Pinus pinaster Ait. and Pinus sylvestris L. trees growing in single-species even-aged stands in northwestern Spain to develop crown profile models. Such models are key components of growth and yield models, and they are also important for assessing competitive level, microclimate, tree vigour, mechanical stability, biological diversity, fire susceptibility and behaviour under wind stress, amongst other features. The equations used in crown profile estimation (i.e. those including crown radius, largest crown radius, height to the largest crown radius and height to the base of the live foliage) were fitted simultaneously to take into account correlations between the different variables. The fitting technique also enabled us to consider an autocorrelated, heteroscedastic error structure and to use a different number of observations for the different variables involved in the fitting process. The fitted models explained between 66 and 94 per cent of the variability in crown radius, with a mean error between 0.15 and 0.64 m. The crown profile models developed can be used to estimate the crown profile when only diameter at breast height, total tree height and height to the base of the live foliage are measured. Inclusion of more variables (such as largest crown radius) provides more accurate resultsSIThis work was financially supported by the Spanish Ministerio de Educación y Ciencia (Project AGL-2004-07976-C02-01) and the Spanish Ministerio de Ciencia e Innovación (Projects AGL-2008-02259/FOR and PSS 310000-2009-22

Consideración de la estabilidad de la masa en diagramas de manejo de la densidad

[ES] Se presenta la estructura de un diagrama de manejo de la densidad (DMD) para las masas de Pinus radiata D. Don en Galicia, considerando la estabilidad de la masa como uno de los posibles objetivos-del régimen de claras. El DMD está compuesto por un sistema de cuatro ecuaciones, el indice de Hart-Becking para caracterizar la espesura y el coeficiente de esbeltez medio de la masa para valorar su estabilidad frente a daños por viento y nieve. El formato de las ecuaciones relaciones está condicionado por las variables a representar en los ejes principales del diagrama (altura dominante en abcisas y número de pies ha en ordenadas) y por la consistencia biológica de las mis-mas. Para la valoración de la estabilidad se incluyeron isolíneas del coeficiente de esbeltez medio de la masa (cociente entre la altura media y el diámetro medio) en el diagrama de manejo. Asimismo. para la representación de los esquemas de claras sobre el diagrama se consideró una disminución del numero de pies debida a la existencia de mortalidad natural por competencia. La inclusión de esta variable permitió obtener evoluciones más realistas de la densidad, sobre todo en el intervalo anterior a la primera claraSIEste trabajo ha sido financiado por el proyecto de investigación AGL2004-07976-C02-0

Modelización de la distribución vertical de combustibles de copa en pies de Pinus pinaster y Pinus radiata en Galicia

[ES] El conocimiento de la distribución vertical de los combustibles de copa en rodales forestales es muy importante, entre otros objetivos, para la determinación de la posibilidad de inicio y de la facilidad de propagación de fuegos de copa. En este trabajo se presentan ecuaciones que permiten estimar la distribución vertical de combustibles de copa en pies de Pinus pinaster Ait. y Pinus radiata D.Don en Galicia. Para desarrollar estas ecuaciones se llevó a cabo un muestreo destructivo de 185árboles (79 de P. pinaster y 106 de P. radiata), situados en las inmediaciones de parcelas permanentes de investigación. En cada parcela se apearon tres árboles correspondientes a las clases sociológicas sumergido, intermedio y codominante/dominante. Una vez apeados, se dividieron en secciones de un metro de longitud, determinándose en cada una de ellas el peso seco correspondiente a las siguientes fracciones: acículas, ramillas (<6 mm de grosor) y ramas (entre 6 y 75 mm de grosor). Mediante técnicas de regresión no lineal se ajustaron simultáneamente modelos para estimar la carga relativa de las diferentes fracciones combustible según la altura relativa del árbol. Los modelos ajustados consiguieron explicar más del 80%de la variabilidad observada para ambas especiesEste trabajo fue financiado por el Ministerio de Ciencia e Innovación (MICINN) a través del proyecto de investigación AGL2008-02259/FO

Biomass and carbon content in Galicia (NW Spain) Eucalyptus globulus Labill. stands

Northwestern Spain is one of the most productive forest areas in Europe, being Eucalyptus globulus Labill. the most important species in the area. Stands (pure and mixed) of the species cover more than 400,000 ha, and almost four million cubic metres of timber were produced annually between 2008 and 2012. In this paper we present estimations of total aboveground biomass and the corresponding carbon content in Eucalyptus globulus plantations in Galicia, as useful information for further analysis on carbon sequestration balance. We developed several easy-to-use biomass equations, using data collected from cut trees across Galicia, and these were applied to data from the Third (1997) and Fourth (2011) National Forest Inventories in the region. The fitted model with diameter and height as independent variables showed the best estimates (R2 Adj = 0.9965, RMSE = 6.28). Estimations of current (2011) total aboveground biomass was 34.8 Mt and for the carbon was 15.7 MtS

Height-diameter models for maritime pine in Portugal: a comparison of basic, generalized and mixed-effects models

Tree height is a key variable in forest monitoring studies and for forest management. However, tree height measurement is time consuming, and the recommended procedure is to use estimates from height-diameter models. Here, we compare height-diameter model forms and approaches for predicting tree height (h) as a function of tree diameter at breast height (d) and additional stand level covariates. Four model forms were evaluated: (i) basic models (which only used d as predictor variable); (ii) generalized models (which used d and stand-level predictor variables); (iii) a mixed-effects model based on the best basic model; and (iv) a mixed-effects model based on the best generalized model. Several alternatives aimed at minimizing height measurement effort were tested in terms of accuracy and applicability. From a practical point of view, the selected generalized model is recommended for estimating the height of maritime pine in Portugal. The results also show that a calibrated basic mixed model provides more accurate results than a basic model locally fitted when the number of h-d observations is limited.S

Desarrollo de un modelo de perfil de copa para Pinus cooperi Blanco en la UMAFOR 1008, Durango, México

A crown profile model for Pinus cooperi Blanco in UMAFOR 1008 (El Salto, Pueblo Nuevo, Durango) was developed from data corresponding to 92 sampled trees. Trees with well-formed crowns were selected from stands varying in age, density and site quality. Diameter at breast height, total height, crown width, crown length, and crown profile were measured in each tree. To predict the crown profile, basic geometric shapes and several mathematic models were evaluated. The model developed by Hann (1999) best described the experimental data of the total crown, light crown, and shaded crown, accounting for over 92 % of the observed variability.Se desarrolló un modelo de perfil de copa para Pinus cooperi Blanco a partir de 92 árboles en la UMAFOR 1008 (Región El Salto, Pueblo Nuevo, Durango). Se seleccionaron individuos con una copa bien conformada y de diferente edad, densidad y calidad de estación. En cada uno de los individuos se midieron las variables diámetro normal, altura total, diámetro, longitud y perfil de copa. Tanto formas geométricas sencillas como algunos modelos matemáticos se analizaron para predecir el perfil de la copa. El mejor modelo para describir el perfil de copa de P. cooperi fue el de Hann (1999), ya que tuvo mejor ajuste para la copa entera, copa de luz y copa de sombra, explicando más de 92 % de la variabilidad de los datos.S