Single-tree Growth Model Research Articles

Analiza izbranih drevesnih modelov razvoja gozdov, primernih za modeliranje na velikoprostorski ravni, in možnosti njihove uporabe v Sloveniji

This article discusses single-tree growth models, which have become an important tool for decision-making, management and strategic decisions in the field of forest management. In Slovenia, we have only recently begun systematic development in the field of forest modelling, which includes the development of a matrix population model, testing selected models from abroad and the development of individual model components. The goal of our work is to introduce the field of empirical single-tree models for modelling forest development on a larger scale. We provide a detailed overview of established methods for modelling individual components of tree models, such as radial and height growth, crown recession, mortality, and recruitment and regeneration. We evaluated the suitability of the selected models from the perspective of their applicability in Slovenia. We conclude that the SILVA, WEHAM, MASSIMO and CALDIS models have the greatest potential for use in Slovenia, as they are all suitable for the different forest types and mixed forests with different structure that prevail in Slovenia. In addition to testing the existing models, we propose the development of new models adapted to the heterogeneous and mixed stands in Slovenia. We also propose expanding the set of indicators in forest inventories and measuring additional tree characteristics, such as canopy characteristics, which would expand forest modelling opportunities in Slovenia. In the conclusions, we also discuss the potential use of machine learning in forest development modelling, as this type of model could represent the next generation of forest models.

Using LiDAR-modified topographic wetness index, terrain attributes with leaf area index to improve a single-tree growth model in south-eastern Finland

Tree growth information is crucial in forest management and planning. Terrain-derived attributes such as the topographic wetness index (TWI), in addition to leaf area index (LAI) are closely related to tree growth, but are not commonly used in empirical growth models. In this study, we examined if modified TWI and LAI estimated from airborne light detection and ranging (LiDAR) data could be used to improve the predictions of a national single-tree diameter growth model. Altogether 1118 sample trees were selected within 197 subjectively placed plots in randomly selected forest stands in south-eastern Finland. Linear mixed effect (LME) and multilayer perceptron models were used to model the bias of 5-year growth predictions of the model and thus ultimately improve its predictions. The root mean square error (RMSE) of the national model was 0.604 cm. LME modelling reduced this value to 0.404 cm and MLP to 0.568 cm. The predictors included in the best-performing LME model were modified TWI, LAI estimated from LiDAR intensities, and elevation. Without an LAI estimate, the best RMSE was 0.436 cm. When applied as such, original and modified TWIs produced similar accuracy. We conclude that both TWI and LAI obtained from LiDAR data improve the diameter growth predictions of the national model.

Temporal Transferability of Pine Forest Attributes Modeling Using Low-Density Airborne Laser Scanning Data

This study assesses model temporal transferability using airborne laser scanning (ALS) data acquired over two different dates. Seven forest attributes (i.e. stand density, basal area, squared mean diameter, dominant diameter, tree dominant height, timber volume, and total tree biomass) were estimated using an area-based approach in Mediterranean Aleppo pine forests. Low-density ALS data were acquired in 2011 and 2016 while 147 forest inventory plots were measured in 2013, 2014, and 2016. Single-tree growth models were used to generate concomitant field data for 2011 and 2016. A comparison of five selection techniques and five regression methods were performed to regress field observations against ALS metrics. The selection of the best regression models fitted for each stand attribute, and separately for both 2011 and 2016, was performed following an indirect approach. Model performance and temporal transferability were analyzed by extrapolating the best fitted models from 2011 to 2016 and inversely from 2016 to 2011 using the direct approach. Non-parametric support vector machine with radial kernel was the best regression method with average relative % root mean square error differences of 2.13% for 2011 models and 1.58% for 2016 ones.

Climate Sensitive Tree Growth Functions and the Role of Transformations

The aim of this study is to develop climate-sensitive single-tree growth models, to be used in stand based prediction systems of managed forest in Switzerland. Long-term observations from experimental forest management trials were used, together with retrospective climate information from 1904 up to 2012. A special focus is given to the role of transformation of modelling basal area increment, helping to normalize the random error distribution. A nonlinear model formulation was used to describe the basic relation between basal area increment and diameter at breast height. This formulation was widely expanded by groups of explanatory variables, describing competition, stand development, site, stand density, thinning, mixture, and climate. The models are species-specific and contain different explanatory variables per group, being able to explain a high amount of variance (on the original scale, up to 80% in the case of Quercus spec.). Different transformations of the nonlinear relation where tested and based on the mean squared error, the square root transformation performed best. Although the residuals were homoscedastic, they were still long-tailed and not normal distributed, making robust statistics the preferred method for statistical inference. Climate is included as a nonlinear and interacting effect of temperature, precipitation and moisture, with a biological meaningful interpretation per tree species, e.g., showing better growth for Abies alba in warm and wet climates and good growing conditions for Picea abies in colder and dryer climates, being less sensitive on temperature. Furthermore, a linear increase in growth was found to be present since the 1940s. Potentially this is an effect of the increased atmospheric CO2 concentration or changed management in terms of reduced nutrient subtractions from forest ground, since industrialization lowered the demand of residue and slash uptake.

LiDAR-based TWI and terrain attributes in improving parametric predictor for tree growth in southeast Finland

The effect of soil moisture content on vegetation and therefore on growth is well known. Information about the growth of forest stands is key in forest planning and management, and is the concern of various stakeholders. One way to assess moisture content and its impacts on forest growth is to apply the Topographic Wetness Index (TWI) and the derived terrain attributes from the Digital Terrain Model (DTM). The TWI is an important terrain attribute, used in various ecological studies. In the current study, a total of 9987 tally trees within 197 sample plots in southeastern Finland and LiDAR (Light Detection and Ranging) −based TWI were selected to examine: 1) the effect of cell resolutions and focal statistics of neighborhood cells of DTM, on tree diameter increment, and 2) possibilities to improve the prediction accuracy of an existing single-tree growth model using the terrain attributes and TWI with the combined effects of three characteristics (i.e., cell resolutions, neighborhood cells and terrain attributes). The results suggest that the TWI with terrain attributes improved the growth estimation significantly, and within different site types the Root Mean Square Errors (RMSE) were lowered substantially. The best results were obtained for birch trees. The higher resolution of the DTM and the lower focal neighborhood cells were found to be the best alternative in computing the TWI.

Implementing Continuous Cover Forestry in Planted Forests: Experience with Sitka Spruce (Picea Sitchensis) in the British Isles

Planted forests of Sitka spruce, a non-native species from north-west America, are the major forest type in Great Britain and Ireland. Standard management involves even-aged stands, rotations of 40–50 years and a patch clear-felling system with artificial regeneration. However, forest policies support managing these forests for multifunctional objectives with increased diversity of species composition and stand structure. Continuous cover forestry (CCF) is an alternative silvicultural approach used to provide such diversity, but the amount of CCF forest is under 10% of the forest area, and less in Sitka spruce forests; This paper reviews research carried out in the last two decades to support the implementation of CCF in Sitka spruce planted forests; Stand structures and microclimate favouring natural regeneration are understood. Harvesting systems have been adapted for use in CCF stands, a single-tree growth model has been calibrated, comparative costs and revenues have been determined, and operational trials established. The interaction between thinning and wind stability in irregular stands is problematic, together with the lack of suitable species for growing in mixture with Sitka spruce; Introduction of an alternative silvicultural approach may take decades and must overcome technical challenges and cultural resistance.

Simulated transformation of even-aged Norway spruce stands to multi-layered forests: an experiment to explore the potential of tree size differentiation

The study investigated the possibility to transform normal young Norway spruce (Picea abies (L.) Karst) forests to develop more heterogeneous stand structures, aiming for multi-layered forest in the long run. On three sites in central and south Sweden, 60 per cent of stand basal area was removed by thinning mainly medium-sized trees and leaving the smallest and the largest trees. Over the next 50 years, future stand development was simulated using a single-tree growth model. Simulations were run with and without ingrowth. An additional ingrowth scenario after soil preparation was tested. Basal area was kept between 10 and 20 m2 ha−1 during simulations. Projected stem wood production for the next 50 years was one-third lower compared with conventional thinning regimes. After 50 years, a multi-layered forest structure was indicated for the boreal sites in central Sweden, but not for the site in south Sweden.

Stochastic or deterministic single-tree models: is there any difference in growth predictions?

Deterministic single-tree models are commonly used in forestry. However, there is evidence that stochastic events may interact with the nonlinear mechanisms that underlie forest growth. As a consequence, stochastic and deterministic simulations could yield different results for the same single-tree model and the same initial conditions. This hypothesis was tested in this study. We used a single-tree growth model that can be implemented either stochastically or deterministically. Two data sets of 186 and 342 plots each were used for the comparisons. For each plot, the simulations were run on a 100-year period using 10-year growth steps. Three different response variables were compared. The results showed that there were differences between the predictions from stochastic and deterministic simulations for some response variables and that randomness alone could not explain these differences. In the case of deterministic simulations, the fact that predictions are reinserted into the model at each growth step is a concern. These predictions are actually random variables and their transformations may result in biased quantities. Forest growth modellers should be aware that deterministic simulations may not correspond to the mathematical expectation of the natural dynamics.

Integrating differentiated landscape preferences in a decision support model for the multifunctional management of the Montado

A great part of the Alentejo region in Southern Portugal is covered by an agro-silvo pastoral system, the Montado. This traditional land-use system is specific, inter alia, in its ability to join production with favorable conditions for non-production functions. At the present time, as society positively evaluates and even demands cultural and amenity functions from the countryside, the Montado management faces the challenge of integrating production with non-production functions in a way which will result in suitable multifunctionality, and a more sound viability of the whole system. The decision support tool (DST) for the cork oak Montado management, the CORKFITS, based on the single-tree growth model and working at the stand level, is oriented primarily to the management of the production functions, but it is able to integrate also other data that can contribute for a more multifunctionality oriented management. In this exploratory study, the integration in the DST, of the preference distribution, as expressed by landscape users is investigated. The aim was to test a more comprehensive functioning of this tool, where non-production functions are also integrated. The described integration intended to communicate to decision-makers how the change in management practices at tree and under cover level, might alter the satisfaction of expectations of different user groups, as such changes affect the composition of the Montado, at both levels. The users considered are those practicing non-production functions in the Montado. Preferences were assessed through a questionnaire survey applied in the region of Alentejo, in the area of dominance of the cork oak, in the Montado system. The non-production functions are, in this context, related particularly to hunting, aesthetic appreciation related to walking and other leisure activities, to life quality, and to tradition and identity, as well as bee-keeping and mushroom picking. This paper focuses on the description of the specific methodological steps applied for the successful integration of the landscape preferences of different user groups into the DST for the cork oak Montado. Integration has proved to be possible, even if some methodological challenges still need to be faced for a more consistent use of the proposed tool.

Estimating growth in beech forests: a study based on long term experiments in Switzerland

• This contribution presents a dynamic stand growth model for Beech (Fagus sylvatica L.) forests, based on a dataset provided by the Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Birmensdorf. The dataset includes 143 research plots, covering a wide range of growing sites and providing up to 16 interval measurements per research plot. • The objective of this research is to complement the range of existing beech growth models by bridging the gap between the historical yield tables and the single tree growth models. The specific aim is to develop transition functions which will project three state variables (dominant height, basal area and number of trees per hectare) at any particular time, in response to any arbitrary silvicultural treatment. • Two of the transition functions were derived using the generalized algebraic difference approach (GADA), the third one was derived with the algebraic difference approach (ADA). All the functions were fitted simultaneously using iterative seemingly unrelated regression and a base-age-invariant method. The influence of thinnings on basal area growth was included by fitting different transition functions for thinned and unthinned stands. • The overall model provides satisfactory predictions for time intervals up to 20 years. The new model is robust and its relatively simple structure makes it suitable for economic analysis and decision support.

Effects of environmental changes on the vitality of forest stands

Using the physiological single tree growth model BALANCE, vitality of forest stands was simulated in dependence of the site-related factors, climate and stand structure. At six level II plots in southern Germany with the main tree species beech (Fagus sylvatica L.), oak (Quercus robur L.), spruce (Picea abies [L.] Karst.), and pine (Pinus sylvestris L.), simulated results were compared to measured values (soil water content, bud burst and leaf colouring, diameter at breast height, tree height and crown density) in order to validate the model. Sensitivity tests were done to examine the influence and the interactions of the environmental parameters. The validation results show that BALANCE is capable of realistically simulating the growth and vitality of forest stands for central European regions for medium term time spans (several years). The validation of the water balance module produces mean absolute errors based on field capacity between 2.7 and 6.9% in dependence of sites and forest stands. Senescence of foliage as well as crown density is reproduced with a correlation coefficient of 0.70 compared to measurements. Differences between measured and simulated diameter values were smaller than 1% for spruce and smaller than 6.5% for beech after 7 years of simulation, and smaller than 1% for oak after 8 years of simulation. On the other hand, the simulations for pine trees conform less with the measurements (difference: 22.6% after 8 years). The sensitivity of the model on environmental changes and on combinations of these parameters could be demonstrated. The responses of the forest stands were quite different.

Growth and population structure of timber species in Peruvian Amazon flood plains

This study provides specific ecological information on growth and population structure of important timber tree species of the Peruvian Amazon flood plains: Guatteria sp., Terminalia oblonga, Hura crepitans, Guarea macrophylla, Maquira coriacea, Virola elongata, Virola pavonis, and Minquartia guianensis. Furthermore, methods that can be applied to study population structure and growth of trees in natural forests are developed upon. The study is based on data collected over a period of 8 years from permanent sample plots covering a total of 18.6 ha in three flood plain forest types at the lower Río Ucayali. The population structure of the eight species varied considerably with maximum diameters at breast height ranging from 31 to 140 cm. For M. coriacea stem densities and basal areas were as high as 159 ha −1 and 3.4 m 2/ha, respectively, but for most other species, stem densities and basal areas were much lower. Seedling densities of the eight species ranged from 1 to 42,002 ha −1 with a mortality of 27–100% per year and for some species a significant relationship was found between mortality and duration of the flooding period. Diameter increments were analyzed using a simple diameter class approach as well as a more sophisticated single-tree growth model, for which a variety of competition indices were screened. Based on the statistical performance and practicability of the indices it appeared that the most successful measure of competition was the local basal area of trees with diameters exceeding that of the individual in question.

Predicting and calibrating diameter distributions of Eucalyptus grandis (Hill) Maiden plantations in Zimbabwe

Diameter distribution models for even-aged Eucalyptus grandis plantations in Zimbabwe were developed using the two-parameter Weibull function. The analysis was based on data from Correlated Curve Trend (CCT) experiments replicated on four different sites. Parameters of the Weibull distribution were predicted using stand characteristics as regressors. Two sets of parameter models were estimated: a set with and one without stand basal area as a predictor. Stand variables such as dominant height, age, site index and number of stems were used in both sets. The models were further calibrated to result in a given number of stems and stand basal area simultaneously. The usability of constructed models was tested both in prediction of yield in a stand inventory situation and in simulation of growth in connection with different growth models. The results indicated that models not including stand basal area produce considerably less precise stand volume estimates compared to models including also stand basal area. Calibration improved the accuracy of diameter distribution models. In growth simulation diameter distribution models can be connected both to single tree growth models and to stand projection models. The usability of calibration in growth simulation depends on the accuracy of the prediction of stand characteristics.

Silvicultural alternatives, competition regime and sensitivity to climate in a European beech forest

Growth variability, expressed by ring width sequences, was examined in an even-aged beech ( Fagus sylvatica L.) forest in relation to stand structure, tree competition and climate. A competition-based growth model was developed to simulate stand dynamics and to calculate the yearly growth index series as a ratio between observed and predicted increments. Dendroclimatological analyses were used to evaluate the interactions between intraspecific competition and tree response to climate. For trees living at different competition levels, simple correlation coefficients were calculated between environmental variables (seasonal values of precipitation, temperature, water deficit and surplus) and the growth index series. Results show that beech response to temperature regime and water availability is significantly affected by competition level. When competition is strong, trees are highly sensitivity to water balance; whereas, at a low competition level, trees react positively to high temperatures. Considering that competition may affect tree sensitivity to climate and that thinnings can modify competition regimes it seems possible to influence the climate response of single trees and whole stands through silvicultural treatments and, consequently, to conduct forest management under a hypothesis of climate change. For this purpose, twenty thinning regimes were simulated with a single-tree growth model, varying the treatment intensity and frequency. Four representative regimes were analysed in detail, by examining the predicted yield and the distribution of trees in competition classes, and by evaluating stand sensitivity to climate change.

An application of a spatial growth model of Scots pine on drained peatland

The study presents a way of adjusting the prediction of a spatial single tree growth model on the basis of the adverse effect of ground water. The spatial distribution of growth resources is described by the depth of the groundwater table and the competition from neighbouring trees. The competition is described by a spatial model made for mineral soils. The depth of the groundwater table is calculated from the local stand volume and the distance from the nearest ditch. The effect of the spatial pattern of trees on the growth of a 25-year old Scots pine ( Pinus sylvestris L.) stand growing on a drained peatland was studied using the simulation model. Heavy clustering of trees decreased the volume growth by 5–13% compared with a regular spatial distribution. Between-tree variation in diameter growth was smallest and the volume growth best when the stand density was about three times higher on the ditch border than in the middle of two adjacent ditches.

Simulation of the development of Norway spruce stands using a transition matrix

The transition-matrix model was applied to a Norway spruce selection forest grown under Finish conditions. The transition probabilities depended on stand density according to a model which was estimated by using empirical single-tree growth models. The dynamics of small seedlings was modelled by adding a separate size class for them to the matrix model. A computer program with comprehensive output was prepared for making simulations. According to the simulations, the selection forest is insensitive to small changes in management and the model is insensitive to small errors in parameters. The volume production of a selection forest is inferior to that of an even-aged stand.

A growth model for red oak in New England

Ecological, silvicultural, and financial equations were used to construct a single tree growth model for red oak (Quercusrubra L.) in New England, U.S.A. A two-phase strategy of forest management is proposed: phase l is early growth at high densities to promote rapid growth of clear boles (merchantable height); phase 2 is a series of thinnings at 10-year intervals to reduce density and so promote stem diameter growth. A dollar value per unit volume is applied to cordwood and sawlog products as a function of product size, and the combination of phase 1 and 2 lengths that maximizes net present value for a sustained series of rotations is determined. Over the range of site indexes 55 to 75, a phase l length of 45 years and total rotation length of 94 to 96 years maximizes financial returns. The trade-off in value growth between merchantable height growth and diameter growth, not the cost of precommercial thinnings, was critical to the determination of the length of phase l. Small changes in phase l length produced large changes in total returns. Rotation length was less sensitive.