Propagating the errors of initial forest variables through stand- and tree-level growth simulators

Developments in the field of remote sensing have led to various cost-efficient forest inventory methods at different levels of detail. Remote-sensing techniques such as airborne laser scanning (ALS) and digital photogrammetry are becoming feasible alternatives for providing data for forest planning. Forest-planning systems are used to determine the future harvests and silvicultural operations. Input data errors affect the forest growth projections and these effects are dependent on the magnitude of the error. Our objective in this study was to determine how the errors typical to different inventory methods affect forest growth projections at individual stand level during a planning period of 30 years. Another objective was to examine how the errors in input data behave when different types of growth simulators are used. The inventory methods we compared in this study were stand-wise field inventory and single-tree ALS. To study the differences between growth models, we compared two forest simulators consisting of either distance-independent tree-level models or stand-level models. The data in this study covered a 2,000-ha forest area in southern Finland, including 240 sample plots with individually measured trees. The analysis was conducted with Monte Carlo simulations. The results show that the tree-level simulator is less sensitive to errors in the input data and that by using single-tree ALS data, more precise growth projections can be obtained than using stand-wise field inventory data.     

Effect of tree-level airborne laser-scanning measurement accuracy on the timing and expected value of harvest decisions

The objective was to compare tree-level airborne laser-scanning (ALS) data accuracy with standwise estimation data accuracy as input data for forest planning, using tree- and stand-level simulators. The influence of the input data accuracy was studied with respect to (1) timing of the next thinning or clear-cutting and (2) the relative variation in the predicted income of the next logging expressed as the net present value (NPV). The timing and predicted NPV of thinning and clear-cutting operations were considered separately. The research was based on Monte Carlo simulations carried out with the tree- and stand-level simulators using a simulation and optimisation (SIMO) framework. The simulations used treewise measurements taken on 270 circular plots measured at the Evo Field Station, Finland, as input data. Deviations in the tree data measured were generated according to the mean standard errors found in standwise field estimation and tree-level ALS. The accuracy factors of ALS individual tree detection were based on the EUROSDR/ISPRS Tree Extraction Project. The results show that input data accuracy significantly affects both the timing and relative NPV of loggings. Tree-level ALS produces more accurate simulation results than standwise estimation with the error levels assumed. Diameter-based characteristics are the most important input data in all simulations. Accurate tree height estimates cannot be fully utilised in current simulators.     

Modelling site quality and individual-tree growth in pure and mixed Pinus brutia stands in north-east Greece

? Simulation tools, based on individual tree growth and mortality models can produce the most detailed predictions of forest stand development under different management schedules. These models allow the manager to predict the development of any type of stand (even- and uneven-aged, and pure and mixed stands).

? Different model approaches and predictors are required for pure even-aged or mixed uneven-aged forest stands. This study developed and compared two sets of models which enable tree-level simulation of the development of pure and mixed stands of Pinus brutia in north-east Greece. The first set of models for even-aged forestry consists of site index models, diameter growth models, tree height models, and mortality models. The second set, which is for uneven-aged forestry, uses a past growth index instead of a site index.

? The simulations and overall fitting statistics suggest that the two types of models provide realistic and accurate predictions of forest stand development and allow one to simulate the development of complex Pinus brutia stand structures in Dadia National Park forests.

? The advantages of the two approaches are discussed and it is suggested that the growth index is an effective predictor of site quality and the set of models which used such variable as predictor performed in a similar way as the models using site index, which require more information and a given stand structure (even-aged).

     

From the Editor

Abstract

For the calculation of carbon balance, estimates of litterfall are needed as a measure of carbon accumulation into soil. Estimation of litterfall should reflect the structural and functional properties of stands that are affected by changes in growing conditions caused, for example, by management activities or climate change. In this context, possibilities taking into account this dynamic relationship between growing conditions and litterfall were analysed by correlating litterfall with growth of trees. As extensive data for modelling this relationship are difficult to obtain, existing literature were analysed to formulate a general model applicable to forestry scenario modelling in practical forest planning under varying conditions. Empirical results from the literature were analysed to ascertain how litterfall is related to the structural and functional properties of tree stands, including the volume growth of stemwood. Further analysis related tree-level growth to litterfall for forest scenario modelling purposes. Data from the literature showed a clear relationship between forest growth and litterfall, and a tree-level linear model was estimated.     

河北省主要树种单木和林分生长率模型研建

利用第六次至第九次全国森林资源清查河北省2001,2006,2011,2016年4个年度的固定样地调查数据,采用非线性回归估计方法,建立了18个树种组的单木胸径生长率和材积生长率模型,以及12个树种组的林分材积生长率模型。结果表明,单木生长率模型的平均预估误差(MPE)基本都在3%以内,而平均百分标准误差(MPSE)、胸径生长率模型大都在10%以内,材积生长率模型大都在20%左右;林分生长率模型的平均预估误差(MPE)基本都在5%以内,平均百分标准误差(MPSE)大都在25%以内。所建模型可为河北省开展森林资源年度更新提供技术支撑。     

Individual-tree diameter growth models for black spruce and jack pine plantations in northern Ontario

Individual-tree distance independent diameter growth models were developed for black spruce and jack pine plantations. Data used in this study came via stem analysis on 1170 black spruce (Picea mariana [Mill.] B.S.P.) and 800 jack pine (Pinus banksiana Lamb.) trees sampled from 75 stands of 25 even-aged monospecific plantations for each species in the Canadian boreal forest region of northern Ontario. Of the 75 stands, 50 were randomly selected for each species and all trees from these stands were used for model development. Trees from the remaining stands were used for model evaluation.A nonlinear mixed-effects approach was applied in fitting the diameter growth models. The predictive accuracy of the models was improved by including random effects coefficients. Four selection criteria - random, dominant or codominant, tree size close to quadratic mean diameter, and small sized - were evaluated for accuracy in predicting random effects for a new stand using the developed models. Random effects predicted based on trees selected using the random selection criterion provided more accurate diameter predictions than those using trees obtained via other selection criteria for both species. The models developed here are very important to forest managers as the diameters predicted by these models or, their stand-level summaries (i.e., basal area, average diameter), are used as inputs in any forest growth and yield models. In addition, individual-tree diameter growth models can be used to directly forecast changes in diameter distribution of stands.     

Do individual-tree growth models correctly represent height:diameter ratios of Norway spruce and Scots pine?

Height:diameter ratios are an important measure of stand stability. Because of the importance of height:diameter ratios for forest management, individual-tree growth models should correctly depict height:diameter ratios. In particular, (i) height:diameter ratios should not exceed that of very dense stands, (ii) height:diameter ratios should not fall below that of open-grown trees, (iii) height:diameter ratios should decrease with increasing spacing, (iv) height:diameter ratios for suppressed trees should be higher than ratios for dominant trees. We evaluated the prediction of height:diameter ratios by running four commonly used individual-tree growth models in central Europe: BWIN, Moses, Silva and Prognaus. They represent different subtypes of individual-tree growth models, namely models with and without an explicit growth potential and models that are either distance-dependent (spatial) or distance-independent (non-spatial). Note that none of these simulators predict height:diameter ratios directly. We began by building a generic simulator that contained the relevant equations for diameter increment, height increment, and crown size for each of the four simulators. The relevant measures of competition, site characteristics, and stand statistics were also coded. The advantage of this simulator was that it ensured that no additional constraint was being imposed on the growth equations, and that initial conditions were identical. We then simulated growth for a 15- and 30-year period for Austrian permanent research plots in Arnoldstein and in Litschau, which represent stands at different age-classes and densities. We also simulated growth of open-grown trees and compared the results to the literature. We found that the general pattern of height:diameter ratios was correctly predicted by all four individual-tree growth models, with height:diameter ratios above that of open-grown trees and below that of very dense stands. All models showed a decrease of height:diameter ratios with age and an increase with stand density. Also, the height:diameter ratios of dominant trees were always lower than that of mean trees. Although in some cases the observed and predicted height:diameter ratios matched well, there were cases where discrepancies between observed and predicted height:diameter ratios would be unacceptable for practical management predictions.     

A variance-covariance structure to take into account repeated measurements and heteroscedasticity in growth modeling

This study proposes a within-subject variance-covariance (VC) structure to take into account repeated measurements and heteroscedasticity in a context of growth modeling. The VC structure integrates a variance function and a continuous autoregressive covariance structure. It was tested on a nonlinear growth model parameterized with data from permanent sample plots. Using a stand-level approach, basal area growth was independently modeled for red spruce (Picea rubens Sarg.) and balsam fir [Abies balsamea (L.) Mill.] in mixed stands. For both species, the implementation of the VC structure significantly improved the maximum likelihood of the model. In both cases, it efficiently accounted for heteroscedasticity and autocorrelation, since the normalized residuals no longer exhibited departures from the assumptions of independent error terms with homogeneous variances. Moreover, compared with traditional nonlinear least squares (NLS) models, models parameterized with this VC structure may generate more accurate predictions when prior information is available. This case study demonstrates that the implementation of a VC structure may provide parameter estimates that are consistent with asymptotically unbiased variances in a context of nonlinear growth modeling using a stand-level approach. Since the variances are no longer biased, the hypothesis tests performed on the estimates are valid when the number of observations is large.     

Predicting stand damage and tree survival in burned forests in Catalonia (North-East Spain)

The study developed models for predicting the post-fire tree survival in Catalonia. The models are appropriate for forest planning purposes. Two types of models were developed: a stand-level model to predict the degree of damage caused by a forest fire, and tree-level models to predict the probability of a tree to survive a forest fire. The models were based on forest inventory and fire data. The inventory data on forest stands were obtained from the second (1989–1990) and third (2000–2001) Spanish national forest inventories, and the fire data consisted of the perimeters of forest fires larger than 20 ha that occurred in Catalonia between the 2nd and 3rd measurement of the inventory plots. The models were based on easily measurable forest characteristics, and they permit the forest manager to predict the effect of stand structure and species composition on the expected damage. According to the stand level fire damage model, the relative damage decreases when the stand basal area or mean tree diameter increases. Conversely, the relative stand damage increases when there is a large variation in tree size, when the stand is located on a steep slope, and when it is dominated by pine. According to the tree level survival models, trees in stands with a high basal area, a large mean tree size and a small variability in tree diameters have a high survival probability. Large trees in dominant positions have the highest probability of surviving a fire. Another result of the study is the exceptionally good post-fire survival ability of Pinus pinea and Quercus suber.     

An approach for examining the effects of preferential uncertainty on the contents of forest management plan at stand and holding level

A proper forest planning process includes the assessment of the decision-makers’ preferences concerning the future forest use. For some owners, it may be a difficult task to express their preferences exactly and in the form that is required for planning calculations. This study presents a new kind of approach for analyzing the effects of preferential uncertainty. The approach consists of examination of the differences in the actual decision variables in forest planning, i.e. selected treatments for stands between holding-level forest plans. In example calculations, the preferential uncertainty was examined from three different viewpoints: the uncertainty in the weights of the objective variables; the uncertainty in the partial utility function; and the combination of these two uncertainty sources. One thousand preference realizations were generated for each of these uncertainty sources. More than one treatment schedules are proposed for stands that are affected by preferential uncertainty. These stands were detected from among the resulting set of 1,000 forest plans. With this done, two potential decision-making strategies, an adaptive behavior strategy and a threshold proportion strategy, were applied as guides in decision-making for stands, which have more than one treatment alternative selected in the produced optimal forest plans. The adaptive behavior technique required that the forest owner select one treatment alternative for at least one stand that has more than one proposed treatment alternative. The treatment alternatives having frequencies exceeding the given threshold frequency were all accepted simultaneously in the threshold strategy. The main benefit of the approach is to present the effects of uncertainties in a way that can be easily understood by the actual decision-makers. It is a promising tool for practical decision-making situations because at least Finnish non-industrial private forest owners quite often focus on making stand-level forest management decisions. It is also suitable for examinations of other uncertainty sources such as timber prices or inventory data.     

Models for Assessing Timber Grade Distribution and Economic Value of Standing Birch Trees

In order to obtain a more precise prediction of the distribution of each timber grade or log grade with regard to the volume of birch (Betula pendula Roth., B. pubescens Ehrh.) in models for long-term planning, ordered probit models were developed. These models were developed by using data from three mixed birch and Norway spruce stands in Norway. The data consisted of 168 stems. In Norway, three ordinary birch saw log grades are commonly used, with pulpwood as a fourth grade. In this study, these four grades were applied in addition to waste timber, which was treated as a fifth grade. The developed models showed that the grade distribution of birch trees of mixed birch and spruce stands was highly correlated with tree height (p<0.01) and height to first visible dry branch (p=0.081). The statistical significance of both models was good (p<0.0001), as measured by log likelihood test statistics. Classifying the 168 stems by saw timber or pulpwood in butt log led to greatly improved estimates (p<0.01). The developed models would allow the incorporation of timber grade in stand simulators, enabling more precise predictions regarding the economic implications of alternative management strategies for birch trees.     

Juvenile diameter distributions of loblolly pine characterized by the two-parameter Weibull function

Diameter distributions of juvenile loblolly pine (Pinus taeda L.) were characterized utilizing a two-parameter Weibull distribution to aid in forecasting and simulation of young stands. Juvenile diameter distributions were studied to gain insight into the effects of various stand-level factors. Results show that diameter distributions in juvenile loblolly pine stands can be successfully characterized with the two-parameter Weibull function. Repeated measures analysis detected significant planting density, age, and age by planting density interaction effects for the scale and shape parameter estimates from the two-parameter Weibull distribution. Using parameter recovery techniques, estimated diameter distributions were derived from easily attainable stand-level characteristics (i.e. basal area per hectare, planting density, age, and quadratic mean diameter). A thorough understanding of juvenile diameter distributions should prove especially useful for operational planning of stands on short rotations that require estimates of productivity at early ages.     

Stand density management diagrams: Review of their development and utility in stand-level management planning

Stand density management diagrams (SDMD's) are average stand-level models which graphically illustrate the relationships between yield, density and mortality throughout all stages of stand development. SDMD's are primarily used to derive density control schedules by management objective and have been developed for numerous, commercially important species, throughout the world. Historically, SDMD's were initially developed by Japanese scientists in the early 1960's. The principal elements of these initial diagrams included size-density relationships representing crown closure, minimum and maximum self-thinning conditions and yield isolines derived from the reciprocal equation of the competition-density effect. During the 1970's and 1980's various modifications to the original modelling approach were proposed including the replacement of the reciprocal equations with empirical-based volume-density functions, employing different relative density indices and size variates, and incorporation of forest production theories. During the early to mid-1990's, SDMD's were developed for a number of additional species employing earlier modelling approaches, including the development of SDMD's for mixed species stands. The objective of this study was to chronologically review the historical development and associated applications of SDMD's in stand-level management planning.     

Modeling top height growth of red alder plantations

Height growth equations for dominant trees are needed for growth and yield projections, to determine appropriate silvicultural regimes, and to estimate site index. Red alder [Alnus rubra Bong.] is a fast-growing hardwood species that is widely planted in the Pacific Northwest, USA. However, red alder dominant height growth equations used currently have been determined using stem analysis trees from natural stands rather than repeated measurements of stand-level top height from plantations, which may cause them to be biased. A regional dataset of red alder plantations was complied and used to construct a dynamic base-age invariant top height growth equation. Ten anamorphic and polymorphic Generalized Algebraic Difference Approach (GADA) forms were fit using the forward difference approach. The Chapman–Richards anamorphic and Schumacher anamorphic model forms were the only ones with statistically significant parameters that yielded biologically reasonable predictions across a full range of the available data. The Schumacher model form performed better on three independent datasets and, therefore, was selected as the final model. The resulting top height growth equations differed appreciably from tree-level dominant height growth equations developed using data from natural stands, particularly at the younger ages and on lower site indices. Both the rate and shape parameters of the Schumacher function were not influenced by initial planting density. However, this analysis indicates that the asymptote, which is related to site index, may be reduced for plantations with initial planting density below 500 trees ha⁻¹. The final equation can be used for predictions of top height (and thus) site index for red alder plantations across a range of different growing conditions.     

From a strategic to a tactical forest management plan using a hierarchic optimization approach

The Finnish state forest enterprise, Metsähallitus, defines the regional harvest levels for a 10-year period in a strategic-level natural resources plan. Although this plan defines stand-level harvest schedules for all stands, in practice, it cannot be used, as the harvests need to be clustered in time and in space. It is applied by giving each subregion goals they need to fulfill in a tactical level planning process, and the harvests are manually clustered into predefined groups of adjacent stands (departments). In this study, we developed a hierarchical optimization process making use of departments for clustering the harvests. For each of the departments, 91 different stand-level harvest schedules (plans) were determined using incomes from one period and the forest value at the end as objectives. The department-level plans were then used as alternatives in a region-level goal optimization problem. The resulting hierarchic plan was compared to the stand-level solution of the strategic-level plan which served as a benchmark plan. The hierarchical plan clustered the harvests and achieved the goals set better than the benchmark plan, but the net present income was 3.3% lower. The approach turned out usable, but further developing of the approach is needed to reduce the costs of clustering.     

Species proportions by area in mixtures of Scots pine (<Emphasis Type="Italic">Pinus sylvestris</Emphasis> L.) and European beech (<Emphasis Type="Italic">Fagus sylvatica</Emphasis> L.)

Scots pine (Pinus sylvestris L.) and European beech (Fagus sylvatica L.) dominate many of the European forest stands. Also, mixtures of European beech and Scots pine more or less occur over all European countries, but have been scarcely investigated. The area occupied by each species is of high relevance, especially for growth evaluation and comparison of different species in mixed and monospecific stands. Thus, we studied different methods to describe species proportions and their definition as proportion by area. 25 triplets consisting of mixed and monospecific stands were established across Europe ranging from Lithuania to Spain in northern to southern direction and from Bulgaria to Belgium in eastern to western direction. On stand level, the conclusive method for estimating the species proportion as a fraction of the stand area relates the observed density (tree number or basal area) to its potential. This stand-level estimation makes use of the potential from comparable neighboring monospecific stands or from maximum density lines derived from other data, e.g. forest inventories or permanent observations plots. At tree level, the fraction of the stand area occupied by a species can be derived from the proportions of their crown projection area or of their leaf area. The estimates of the potentials obtained from neighboring monospecific stands, especially in older stands, were poorer than those from the maximum density line depending on the Martonne aridity index. Therefore, the stand-level method in combination with the Martonne aridity index for potential densities can be highly recommended. The species’ proportions estimated with this method are best approximated by the proportions of the species’ leaf areas. In forest practice, the most commonly applied method is an ocular estimation of the proportions by crown projection area. Even though the proportions of pine were calculated here by measuring crown projection areas in the field, we found this method to underestimate the proportion by 25% compared to the stand-level approach.     

Integrating pine honeydew honey production into forest management optimization

Pine honeydew honey is an economically important non-wood forest product from eastern Mediterranean Pinus brutia forests, which are also important for timber production. Pine honey is produced by bees that feed on the honeydew secretions of Marchalina hellenica, a scale insect that infests pine stands and feeds on pine sap. The aim of this study was to optimize the joint production of pine honeydew honey and timber by maximizing the soil expectation value of pine stands. The simulation of P. brutia stand dynamics and timber production in healthy and infested stands is based on individual-tree growth and yield models that account for the effect of M. hellenica on tree- and stand-level growth and mortality. The optimization procedure uses a direct search method based on nonlinear programming. The results suggest that pine stands growing on good sites should be managed using rather short rotations and mainly aiming at timber production. In contrast, forest management in medium- and poor-quality sites should aim at longer rotations by taking advantage of the joint production of pine honey and timber assortments. Honey-oriented forest management can be much more profitable than timber production in stands growing on medium and poor sites. Pine honey represents an opportunity to increase the value and economic profitability of P. brutia forests.     

A forest planning model for continuous employment in a forested village with primarily young stands in Korea

This paper presents a practical forest planning approach for continuous forest-based employment in a forested village with primarily young stands. The model is designed to find the practice level for continuous forest employment which embraces both the goal of maximizing the total forest employment and the constraint of maintaining its annual balance, considering forest size and condition, and budget available for forest practice. Through controlling the practice level with the help of a desired employment effect that contributes to allocating forest practices equally to each plan year, a marginal practice level can be found under which any practice level fulfills the goal and constraints. The potential practice area, which is determined by forest area, stand age, and practice schedule, contributes to determining the area silviculturally available for forest practice. Our forest planning model is focused on the planning of young forests which are not expected to yield merchantable products in the near term. The model can also be characterized by landscape-level forest planning in which stand-level practices are planned for achieving a forest-level goal of continuous forest employment. Thus, the model can serve as a basic planning tool for maintaining healthy forests as well as continuous forest employment in young forest areas, where forest-level goals are predicated on stand level practices.     

Evaluation of forest growth simulators with NFI permanent sample plot data from Finland

Tree-level and stand-level forest growth simulators and their combination were evaluated using data from a large network of permanent sample plots of the National Forest Inventory covering the whole of Southern Finland. The simulators were built up with the SIMO framework. The evaluation was carried out both at the stand-level and separately for Scots pine (Pinus sylvestris), Norway spruce (Picea abies), silver birch (Betula pendula) and white birch (Betula pubescens) strata within the plots. Effects of different factors, e.g. age, soil type, stand density and geographical location on the results were also analysed.