In addition to dbh, total tree height and upper-stem diameter have been commonly used to improve tree stem volume estimation. However, measurement error in these variables has not been accounted for ...when realized gains on estimating stem volume are assessed. The aim of this study was to evaluate whether height and upper-stem diameter actually improve accuracy of volume estimation when measurement error is considered and its effect on prediction. dbh was considered to be observed without measurement error. For this analysis, a volume equation and three stem taper functions (with two algebraic constraining alternatives) were fitted and applied over four data sets of stem measurements from loblolly pine stands. Several levels of variability of measurement errors were assessed using a Monte Carlo simulation approach. These conditional predictor variables improved volume prediction when no measurement error was considered, as expected. However, as measurement error increased, the accuracy of volume estimation decreased. When the three variables were considered for volume estimation, measurement error in height caused a positive bias, whereas that corresponding to upper-stem diameter yielded a negative bias. Finally, in terms of volume prediction, inclusion of height clearly justifies the effort needed to measure it, whereas inclusion of upper-stem diameter is only recommended if its measurement error is low.
CONTEXT : Taper equations predict the variation in diameter along the stem, therefore characterizing stem form. Several recent studies have tested mixed models for developing taper equations. ...Mixed-effects modeling allow the interindividual variation to be explained by considering both fixed-effects parameters (common to the population) and random-effects parameters (specific to each individual). AIMS : The objective of this study is to develop a mixed-effect variable exponent taper equation for birch trees in northwestern Spain by determining which fixed-effects parameters should be expanded with random-effects parameters. METHODS : All possible combinations of linear expansions with random effects in one and in two of the fixed-effects model parameters were tested. Upper stem diameter measurements were used to estimate random-effects parameters by the use of an approximate Bayesian estimator, which calibrated stem profile curves for individual trees. RESULTS : Parameter estimates for more than half of the mixed models investigated were nonsignificant. A first order autoregressive error structure was used to completely remove the autocorrelation between residuals, as mixed-effects modeling were not sufficient for this purpose. CONCLUSION : The mixed model with the best fitting statistics did not provide the best calibration statistics for all upper stem diameter measurements. From a practical point of view, model calibration should be considered an essential criterion in mixed model selection.
Since Parresol's (Can. J. For. Res. 31:865- 878, 2001) seminal article on the topic, it has become standard to develop nonlinear tree biomass equations to ensure compatibility among total and ...component predictions and to fit these equations using multistep generalized least-squares methods. In particular, many studies have specified equations for total tree biomass by aggregating the expectations of M component biomass models and have fit all M + 1 equations jointly using seemingly unrelated regression. More recently, an alternative approach has been used wherein compatibility is ensured by deriving multiplicative component expectations, with estimation carried out using instrumental variables and generalized least squares. Yet neither of these strategies considers the fundamental additivity of biomass data themselves nor the implied stochastic constraints necessary for maximum likelihood (ML) estimation. For model selection based on information criteria, stochastic simulation, Bayesian inference, or estimation with missing data, it is important to base estimation and inference on valid probabilistic models. Here, we show how aggregative and disaggregative nonlinear equations can be specified within a probabilistic framework and fit using Gaussian ML with open-source software. We use Parresol's slash pine (Pinus elliottii Engelm. var. elliottii) data to contrast model forms and predictions. We also show how the ML approach can accommodate unobserved or aggregated component biomass data and can thus be useful for integrating felled-tree data collected under different protocols.
•We propose a new metric for measuring even-flow in forest planning.•We rigorously analyze the mathematical properties of the new metric.•We compare the use of gradient-based and free-gradient ...methods with this metric.•We maximize even-flow in a real case study.
In this work we deal with the mathematical analysis of a new metric for measuring even-flow in even-aged forest management planning. We begin writing the most used way of measuring even-flow, and showing the main disadvantages of this classical procedure. Next, we introduce the new metric and study the regularity of the corresponding function, which results to be continuous and to have continuous derivatives in almost all points. We give an explicit expression for these derivatives and analyze its usefulness by comparing a gradient-type method with a derivative-free algorithm (widely used in forestry) to maximize even-flow in a forest of 51 Eucalyptus globulus Labill. stands in Galicia (NW Spain). We observe that gradient-type methods work well with the new even-flow metric, which enables this type of methods for solving the multi-objective problems that can be formulated in forest planning.
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 planning.
▶ Data obtained at irregular measurement intervals and containing missing observations complicate fitting of individual-tree growth models. ▶ A variable growth rate approach, which allows growth and ...mortality to vary year to year, is useful in fitting such models. ▶ Weighted regression allows dealing with different number of observations for different dependent variables in simultaneous model fitting. ▶ The combination of these two techniques allows the development of an individual-tree growth model, fitting simultaneously a basal area growth equation, a height growth equation and a mortality equation.
An individual-tree growth model was developed with data from 54 permanent plots of Scots pine (
Pinus sylvestris L.) located in Galicia (northwestern Spain). The study involved two model fitting approaches, one considering constant growth and mortality rates in the period between two consecutive inventories, and another considering variable growth and mortality rates in the same period. The individual-tree growth model was based on annual basal area growth, height growth and survival probability. The model included variables from groups pertaining to tree size, competition and age. Weighted regression was used as a tool for dealing with missing height observations in model fitting. Evaluation of the model via simulation of growth and mortality in the period between inventories showed that the variable growth rate approach provided slightly better results than the constant growth rate approach. The final model was consistent with expected diameter growth, height growth, dominant height growth, stand basal area growth and reduction in number of stems per hectare.
•Aboveground biomass, carbon and nutrients were quantified in pedunculate oak.•Six harvesting methods were simulated in an average oak stand at rotation age.•Harvesting oak can remove a specific ...nutrient further than other fast-growing species.•Differences in nutrient extraction depend on the species, nutrient and harvesting method considered.
In northern Spain, the use of biomass to produce bioenergy has led to increased exploitation of both natural pedunculate oak (Quercus robur L.) stands and fast-growing plantations of natural or exotic species. In this study, we developed a model for estimating aboveground biomass, carbon and nutrient contents in different pedunculate oak components at individual-tree and at stand level. Six harvesting methods were simulated in an average stand, ranging from whole-tree to stem wood extraction (stem without bark) and including the conventional harvesting method used in the region (extraction of stem plus branches of diameter >7cm). The biomass and macronutrients extracted were compared with those removed during harvesting of fast-growing tree species (Eucalyptus globulus Labill., Pinus radiata D. Don and Pinus pinaster Ait.) on the same temporal basis (mean annual values). Harvesting pedunculate oak stands generally extracted lower amounts of nutrients than harvesting fast-growing species, although the differences depended on the species, macronutrients and harvesting regime considered.
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 projections.
âKEY MESSAGE : A dynamic growth model was developed for maritime pine in Asturias. During the evaluation process, a stand volume ratio function proved the best of two alternative methods for ...estimating merchantable volume. Comparison of the developed model with existing models for nearby regions showed that a single model may suffice for the whole of the NW Iberian Peninsula. âCONTEXT : Maritime pine is one of the most important tree species in NW Spain. There was no existing dynamic growth model for this species in Asturias. âAIMS : To develop a dynamic growth model for maritime pine in Asturias, by evaluating two different methods of estimating volume (a disaggregation system and a stand volume ratio function), and to compare the developed model with existing models for Galicia and northern Portugal are the goals of this study. âMETHODS : The dynamic model is based on the state-space approach, in which three state variables characterize the stand at any point in time: dominant height, number of stems per hectare and stand basal area. The transition function for the first variable was developed on the basis of stem analysis data in a previous study, while the corresponding functions for the last two variables were simultaneously fitted with data obtained from successive measurements of permanent plots. An appendix outlining the implementation of a stand growth simulator in the R environment is included to facilitate model use and evaluation. âRESULTS : When the whole model was used to project the stand conditions, the stand volume ratio function performed best, yielding a root mean square error of 22.4 m³ haâ»Â¹ and a critical error of 18.4 %. Comparison with models developed for other regions revealed both similarities and differences, some of which may be attributed to an unequal distribution of the available data in age and site quality classes. âCONCLUSION : The proposed dynamic growth model provided accurate results, and comparison with other region-specific models showed that a single dynamic model may suffice for the whole of the NW Iberian Peninsula.
Key message
Site form and site index have shown similar precision for estimating site quality in even-aged
Pinus radiata
D. Don stands in north-western Spain. Additionally, SF presents the advantage ...that it does not require stand age information and can therefore be used in a wider set of situations in the forestry practice.
Context
Estimation of site quality is essential for characterizing, monitoring and predicting forest resources. Site index (i.e. the dominant height of the stand at a reference age) is ordinarily used to estimate site quality; however, this index is only useful for even-aged stands of known age. By contrast, SF is age-independent as it uses the dominant height of the stand at a reference dominant diameter.
Aims
The aim of this study was to compare the performance of SF and SI for site quality estimation in even-aged
P. radiata
stands.
Methods
Dynamic equations derived with the Generalized Algebraic Difference Approach (GADA) from the Hossfeld IV base model were fitted to predict site quality with both SI and SF. SF predictions were compared with SI regarding variability within the same plot and consistency in site quality predictions, using the observed maximum mean annual volume increment (MAI) as a direct measure of site quality.
Results
Both approaches showed good performance in model fitting and provided similar goodness-of-fit statistics and variability in the predictions. However, SI performed slightly stronger when related to MAI.
Conclusion
SF performed adequately in estimating site quality for even-aged
P. radiata
stands, with results comparable to those obtained using traditional SI.
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