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

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

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

Above-ground biomass equations for Pinus radiata D. Don in Asturias

Aim of the study: The aim of this study was to develop a model for above-ground biomass estimation for Pinus radiata D. Don in Asturias. Area of study: Asturias (NE of Spain). Material and methods: Different models were fitted for the different above-ground components and weighted regression was used to correct heteroscedasticity. Finally, all the models were refitted simultaneously by use of Nonlinear Seemingly Unrelated Regressions (NSUR) to ensure the additivity of biomass equations. Research highlights: A system of four biomass equations (wood, bark, crown and total biomass) was develop, such that the sum of the estimations of the three biomass components is equal to the estimate of total biomass. Total and stem biomass equations explained more than 92% of observed variability, while crown and bark biomass equations explained 77% and 89% respectively.This study was funded by the Asturian Energy Foundation (FAEN) and the Regional Ministry of Rural Environment and Fisheries (Government of the Principality of Asturias) through the project CN-06-007 "Production of biomass in several forestry species in Asturias"S

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

Fitting and calibrating a multilevel mixed-effects stem taper model for maritime pine in NW Spain

Stem taper data are usually hierarchical (several measurements per tree, and several trees per plot), making application of a multilevel mixed-effects modelling approach essential. However, correlation between trees in the same plot/stand has often been ignored in previous studies. Fitting and calibration of a variable-exponent stem taper function were conducted using data from 420 trees felled in even-aged maritime pine (Pinus pinaster Ait.) stands in NW Spain. In the fitting step, the tree level explained much more variability than the plot level, and therefore calibration at plot level was omitted. Several stem heights were evaluated for measurement of the additional diameter needed for calibration at tree level. Calibration with an additional diameter measured at between 40 and 60% of total tree height showed the greatest improvement in volume and diameter predictions. If additional diameter measurement is not available, the fixed-effects model fitted by the ordinary least squares technique should be used. Finally, we also evaluated how the expansion of parameters with random effects affects the stem taper prediction, as we consider this a key question when applying the mixed-effects modelling approach to taper equations. The results showed that correlation between random effects should be taken into account when assessing the influence of random effects in stem taper predictionThe corresponding author was in receipt of an FPU grant (AP2012-05337) from the Spanish Ministry of Education, Culture and Sport, http://www.mecd.gob.es/. This work was also supported by project no. AGL2008-02259/FOR from the Spanish Ministry of Science and Innovation, http://www.idi.mineco.gob.es/; and project nos. CN-07-094 and SVPA-13-ECOEMP-58 from the Government of the Principality of Asturias, http://www.asturias.es/S

Dynamic Stand Model for Eucalyptus globulus (L.) in Uruguay

Los modelos dinámicos a nivel de rodal son ampliamente usados en el ámbito forestal. Para su ajuste se emplean datos empíricos que se integran en un conjunto de ecuaciones que describen las relaciones entre diferentes variables. Las metodologías clásicas para desarrollar ecuaciones de transición invariantes con respecto al intervalo de simulación (path invariance) e invariantes respecto a la edad de referencia empleadas son algebraic difference approach (ADA) y generalized algebraic difference approach (GADA). El objetivo de este trabajo fue desarrollar un modelo dinámico de rodal para Eucalyptus globulus, empleando ecuaciones de transición para área basal, altura media dominante y mortalidad, utilizando enfoque de variables dummy. Los datos utilizados provienen de 168 parcelas permanentes. Las ecuaciones evaluadas individualmente fueron luego ajustadas simultáneamente mediante seemingly unrelated regression (SUR). En base al análisis de bondad de ajuste y de la capacidad predictiva, se seleccionó el modelo propuesto por Korf, modificado por Cieszewski (2004), para la altura media dominante; el modelo de Levakovic (Zeide, 1993), para el área basal y el modelo de Pienaar y Shiver (1981) para la mortalidad. El modelo de simulación desarrollado es más flexible y permite levantar algunas de las limitantes del modelo utilizado anteriormente. Su integración a sistemas de apoyo a la toma de decisiones constituirá una herramienta de gran utilidad para la planificación y toma de decisiones en el sector forestal.Stand level dynamic models are widely used in forestry. Fitting empirical data that is integrated into a set of equations is used to describe the relationships between different variables The classic methodologies to develop equations invariant with respect to transition simulation interval (path invariance) and invariant respect to the reference age are employed algebraic difference approach (ADA) and generalized algebraic difference approach (GADA). The aim of this study was to develop a dynamic model for Eucalyptus globulus stand using transition equations for basal area, dominant average height and mortality, using tle dummy variables approach. The data used are from 168 permanent plots. The equations evaluated individually were then adjusted simultaneously by seemingly unrelated regression (SUR). Based on the analysis of goodness of fit and predictive ability, the model proposed by Korf, as amended by Cieszewski (2004), for the dominant average height was selected; Levakovic model (Zeide, 1993) for the basal area and the model Pienaar and Shiver (1981) for mortality. The simulation model developed is more flexible and can lift some of the limitations of the model used previously. Its integration into a decision support system (DSS), constitute a useful tool for planning and decision making in the forestry sector.S

A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiata and Pinus sylvestris stands in northwest Spain

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 Burkhart’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 methodEl 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 apropiadoThe present study was financially supported by the Gobierno del Principado de Asturias with the projects: “Estudio del crecimiento y producción en pinares regulares de Pinus radiata D. Don. en Asturias (PC04- 57)” and “Estudio del crecimiento y producción de Pinus pinaster Ait. en Asturias (CN-07-094)”; and by the Comisión Interministerial de Ciencia y Tecnología (CICYT) and the Comisión Europea with the projects: “Repoblación y gestión selvícola de Pino radiata y Pino de Oregón en Galicia (1FD97-0585-C03-03)” and “Crecimiento y evolución de masas de pinar en Galicia (AGL2001-3871-C02-01)”S