Height-diameter relationships for Scots pine plantations in Bulgaria: optimal combination of model type and application

The height-diameter relationship is an important and extensivelyinvestigated forest model, but generalized and mixed-effects models of wider applicability are currently lacking in the forest modeling literature for Scots pine (Pinus sylvestris L.) plantations in Bulgaria. Considering the practical advantages of deterministic and mixed-effects models, the present study aims to derive a generalized deterministic height-diameter relationship and a simple mixed-effects model for plantation-grown Scots pine in Bulgaria. Ten generalized and six local models of adequate mathematical properties were selected and examined in several subsequent steps with a representative data set.A deterministic model was derived for tree height reconstruction fromthe individual tree diameters, stand dominant height and diameter,number of trees per hectare and stand age. Mixed-effects models weredeveloped from the individual-tree and stand diameters and heights applicable to determine the height-diameter relationship in field surveys. Both types of models can be applied with confidence, according to their advantages and specifications, for estimating the height-diameter relationship of Scots pine plantations in Bulgaria, presenting a unique contribution for the particular species, study area and type of model. The choice of the tested models is relevant to the height-diameter relationship investigation of biologically related and geographically close species and types of stands and the study procedure allows repetition of the work to provide reliable solutions of the problem where information on such type of model is deficient or incomplete

Delimiting the spatio-temporal uncertainty of climate-sensitive forest productivity projections using Support Vector Regression

As climate change makes many traditional empirical growth approaches not functional for forest dynamics modelling, new climate-sensitive models are needed. However, using these newly developed models for extrapolation, such as predicting forest productivity for new areas or future scenarios is still a difficult task. In this study, we proposed a method for delimiting the uncertainty of climate-sensitive extrapolations of forest productivity (site index, ) using the regularisation approach implicit in distance-based Support Vector Regression. As a case study, we predicted forest productivity with a dataset of 165 permanent research plots of radiata pine forests in Galicia (NW of Spain) as a function of bioclimatic variables from the Worldclim 2 raster datasets. The developed model was based on the radial basis kernel and, after calibrating it using cross-validation, produced adequate performance metrics, explaining up to 56% of the site index’ variability. Then, we predicted forest productivity for the Galician territory basing on climate raster maps for current conditions and six future scenarios (using different Global Climate Models) and evaluated the resulting maps by delimiting the surfaces with predictions strongly regressed to the mean. This analysis revealed that the extrapolations for unseen climatic conditions were extremely regularised, even for current climate, being 60–99% of the territory regressed to the observational site index mean. In other words, the validity area delimited for the fitted model was narrow in comparison with the prediction extent. These results imply that the climatic conditions in these areas/scenarios were too different from the training datastet for making reliable predictions, at least under the optimum model setup defined by cross-validation. However, when we reduced the parameter, responsible for controlling distance-based regularisation, we observed a noticeable increase in validity area of the model, together with a drop in performance. This fact revealed the existence of a trade–off between highly specific models, with high performance and a small applicability area, and more generalisable models, with a broad validity area but lower performance. We concluded that the tested methodology could be a useful starting point for assessing the spatio-temporal uncertainty of forest productivity predictions in the futureThe work of the first author and main researcher of this study has been partially funded by the Spanish Ministry of Science, Innovation and Universities (DI-16–08971) and by the forest management consultancy company CERNA Ingeniería y Asesoría Medioambiental S.L. Plot data collection was carried out in the frame of two research projects (AGL2008-02259 and AGL2001-3871-C02-01) funded by the Spanish Ministry of Science and Innovation, the Spanish Interdepartmental Commission of Science and Technology and the European Commission (European Regional Development Fund)S

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

Distance-independent individual tree diameter-increment model for Thya (Tetraclinis articulata (VAHL.) MAST.) stands in Tunisia

Aim of study: The aim of the work was to develop an individual tree diameter-increment model for Thuya (Tetraclinis articulata) in Tunisia. Area of study: The natural Tetraclinis articulata stands at Jbel Lattrech in north-eastern of Tunisia. Material and methods: Data came from 200 trees located in 50 sample plots. The diameter at age t and the diameter increment for the last five years obtained from cores taken at breast height were measured for each tree. Four difference equations derived from the base functions of Richards, Lundqvist, Hossfeld IV and Weibull were tested using the ageindependent formulations of the growth functions. Both numerical and graphical analyses were used to evaluate the performance of the candidate models. Main results: Based on the analysis, the age-independent difference equation derived from the base function Richards model was selected. Two of the three parameters (growth rate and shape parameter) of the retained model were related to site quality, represented by a Growth Index, stand density and the basal area in larger trees divided by diameter of the subject tree expressing the inter-tree competition. Research highlights: The proposed model can be useful for predicting the diameter growth of Tetraclinis articulata in Tunisia when age is not available or for trees growing in uneven-aged stands

Un modèle de croissance pour des peuplements de Pinus radiata D. Don du nord ouest de l’Espagne

[EN] A dynamic whole-stand growth model for radiata pine (Pinus radiata D. Don) stands in north-western Spain is presented. In this model, the initial stand conditions at any point in time are defined by three state variables (number of trees per hectare, stand basal area and dominant height), and are used to estimate total or merchantable stand volume for a given projection age. The model uses three transition functions derived with the generalized algebraic difference approach (GADA) to project the corresponding stand state variables at any particular time. These equations were fitted using the base-age-invariant dummy variables method. In addition, the model incorporates a function for predicting initial stand basal area, which can be used to establish the starting point for the simulation. Once the state variables are known for a specific moment, a distribution function is used to estimate the number of trees in each diameter class by recovering the parameters of the Weibull function, using the moments of first and second order of the distribution. By using a generalized height-diameter function to estimate the height of the average tree in each diameter class, combined with a taper function that uses the above predicted diameter and height, it is then possible to estimate total or merchantable stand volume[FR] Un modèle dynamique de croissance de peuplement est présenté pour Pinus radiata D. dans le nord ouest de l’Espagne. Dans ce modèle, les conditions initiales du peuplement en tout point et temps sont définies par trois variables d’état (nombre d’arbres à l’hectare, surface terrière et hauteur dominante) et sont utilisées pour estimer le volume total ou marchand du peuplement pour un âge donné. Le modèle utilise trois fonctions de transition dérivées avec une approche par différence algébrique généralisée (GADA) pour projeter les variables d’état correspondantes du peuplement à n’importe quel moment. Ces équations ont été ajustées en utilisant la méthode des variables indicatrices indépendantes de l’âge. En plus, le modèle incorpore une fonction de prédiction de la surface terrière initiale du peuplement qui peut être utilisée pour établir le point de départ de la simulation. Une fois que les variables d’état sont connues à un instant donné, une fonction de distribution est utilisée pour estimer le nombre d’arbres dans chaque classe de diamètre en récupérant les paramètres de la fonction de Weibull, en utilisant les moments de premier et de second ordre de la distribution. En utilisant une fonction généralisée hauteur-diamètre pour estimer la hauteur de l’arbre moyen de chaque classe de diamètre, combinée avec une fonction qui utilise la prédiction précédente du diamètre et de la hauteur, il est alors possible d’estimer le volume total ou marchand du peuplementSIThis study was financed by the Spanish Ministry of Education and Science; project No AGL2004-07976-C02-

Multi-objective models for the forest harvest scheduling problem in a continuous-time framework

In this study we present several multi-objective models for forest harvest scheduling in forest with single-species, even-aged stands using a continuous formulation. We seek to maximize economic profitability and even-flow of timber harvest volume, both for the first rotation and for the regulated forest. For that, we design new metrics that allow working with continuous decision variables, namely, the harvest time of each stand. Unlike traditional combinatorial formulations, this avoids dividing the planning horizon into periods and simulating alternative management prescriptions before the optimization process. We propose to combine a scalarization technique (weighting method) with a gradient-type algorithm (L-BFGS-B) to obtain the Pareto frontier of the problem, which graphically shows the relationships (trade-offs) between objectives, and helps the decision makers to choose a suitable weighting for each objective. We compare this approach with the widely used in forestry multi-objective evolutionary algorithm NSGA-II. We analyze the model in a Eucalyptus globulus Labill. forest of Galicia (NW Spain). The continuous formulation proves robust in forests with different structures and provides better results than the traditional combinatorial approach. For problem solving, our proposal shows a clear advantage over the evolutionary algorithm in terms of computational time (efficiency), being of the order of 65 times faster for both continuous and discrete formulationsS

Comparación de métodos de estimación de ajuste de las funciones Weibull, SB de Johnson y beta a masas de Pinus pinaster, Pinus radiata y Pinus sylvestris en el noroeste de España

The purpose of this study was to compare the accuracy of the Weibull, Johnson’s SB and beta distributions, fitted with some of the most usual methods and with different fixed values for the location parameters, for describing diameter distributions in even-aged stands of Pinus pinaster, Pinus radiata and Pinus sylvestris in northwest Spain. A total of 155 permanent plots in Pinus sylvestris stands throughout Galicia, 183 plots in Pinus pinaster stands throughout Galicia and Asturias and 325 plots in Pinus radiata stands in both regions were measured to describe the diameter distributions. Parameters of the Weibull function were estimated by Moments and Maximum Likelihood approaches, those of Johnson’s SB function by Conditional Maximum Likelihood and by Knoebel and Burhart’s method, and those of the beta function with the method based on the moments of the distribution. The beta and the Johnson’s SB functions were slightly superior to Weibull function for Pinus pinaster stands; the Johnson’s SB and beta functions were more accurate in the best fits for Pinus radiata stands, and the best results of the Weibull and the Johnson’s SB functions were slightly superior to beta function for Pinus sylvestris stands. However, the three functions are suitable for this stands with an appropriate value of the location parameter and estimation of parameters method.El objetivo de este estudio fue comparar la precisión de las distribuciones Weibull, SB de Johnson y beta, ajustadas por alguno de los métodos más habituales y fijando diferentes valores para los parámetros de localización, para describir distribuciones diamétricas en masas regulares de Pinus pinaster, Pinus radiata y Pinus sylvestris en el noroeste de España. Se midieron un total de 155 parcelas permanentes en masas de Pinus sylvestris en Galicia, 183 parcelas de Pinus pinaster en Galicia y en Asturias y 325 parcelas de Pinus radiata en ambas regiones para describir sus distribuciones diamétricas. Los parámetros de la función Weibull fueron estimados por las aproximaciones de los Momentos y Máxima Verosimilitud, los de la función SB de Johnson por los estimadores condicionados de Máxima Verosimilitud y por el método de Knoebel y Burkhart, y los de la función beta por el método basado en los Momentos de la distribución. Las funciones beta y SB de Johnson fueron ligeramente superiores a la función Weibull en las masas de Pinus pinaster; las funciones SB de Johnson y beta fueron más precisas en los mejores ajustes en las masas de Pinus radiata, y los mejores resultados de las funciones Weibull y SB de Johnson fueron ligeramente superiores a los de la función beta en las masas de Pinus sylvestris. No obstante, las tres funciones son apropiadas para estas masas siempre que se elija un valor de localización y método de estimación de los parámetros apropiado

Simultaneous optimization of even flow and land and timber value in forest planning: a continuous approach

Background: Forest management planning involves deciding which silvicultural treatment should be applied to each stand and at what time to best meet the objectives established for the forest. For this, many mathematical formulations have been proposed, both within the linear and non-linear programming frameworks, in the latter case generally considering integer variables in a combinatorial manner. We present a novel approach for planning the management of forests comprising single-species, even-aged stands, using a continuous, multi-objective formulation (considering economic and even flow) which can be solved with gradient-type methods. Results: The continuous formulation has proved robust in forest with different structures and different number of stands. The results obtained show a clear advantage of the gradient-type methods over heuristics to solve the problems, both in terms of computational time (efficiency) and in the solution obtained (effectiveness). Their improvement increases drastically with the dimension of the problem (number of stands). Conclusions: It is advisable to rigorously analyze the mathematical properties of the objective functions involved in forest management planning models. The continuous bi-objective model proposed in this paper works with smooth enough functions and can be efficiently solved by using gradient-type techniques. The advantages of the new methodology are summarized as: it does not require to set management prescriptions in advance, it avoids the division of the planning horizon into periods, and it provides better solutions than the traditional combinatorial formulations. Additionally, the graphical display of trade-off information allows an a posteriori articulation of preferences in an intuitive way, therefore being a very interesting tool for the decision-making process in forest planningS

Forecasting variations in profitability and silviculture under climate change of radiata pine plantations through differentiable optimization

Climate change might entail significant alterations in future forest productivity, profitability and management. In this work, we estimated the financial profitability (Soil Expectation Value, SEV) of a set of radiata pine plantations in the northwest of Spain under climate change. We optimized silvicultural interventions using a differentiable approach and projected future productivity using a machine learning model basing on the climatic predictions of 11 Global Climate Models (GCMs) and two Representative Concentration Pathways (RCPs). The forecasted mean SEV for future climate was lower than current SEV (∼22% lower for RCP 4.5 and ∼29% for RCP 6.0, with interest rate = 3%). The dispersion of the future SEV distribution was very high, alternatively forecasting increases and decreases in profitability under climate change depending on the chosen GCM. Silvicultural optimization considering future productivity projections effectively mitigated the potential economic losses due to climate change; however, its ability to perform this mitigation was strongly dependent on interest rates. We conclude that the financial profitability of radiata pine plantations in this region might be significantly reduced under climate change, though further research is necessary for clearing the uncertainties regarding the high dispersion of profitability projectionsS