Evaluation of different approaches to individual tree growth and survival modelling using data collected at irregular intervals - a case study for Pinus patula in Kenya

Background： The minimum set of sub-models for simulating stand dynamics on an individual-tree basis consists of tree-level models for diameter increment and survival. Ingrowth model is a necessary third component in uneven-aged management. The development of this type of model set needs data from permanent plots, in which all trees have been numbered and measured at regular intervals for diameter and survival. New trees passing the ingrowth limit should also be numbered and measured. Unfortunately, few datasets meet all these requirements. The trees may not have numbers or the length of the measurement interval varies. Ingrowth trees may not have been measured, or the number tags may have disappeared causing errors in tree identification. Methods： This article discussed and demonstrated the use of an optimization-based approach to individual-tree growth modelling, which makes it possible to utilize data sets having one or several of the above deficiencies. The idea is to estimate all parameters of the sub-models of a growth simulator simultaneously in such a way that, when simulation begins from the diameter distribution at the first measurement occasion, it yields a similar ending diameter distribution as measured in the second measurement occasion. The method was applied to Pinus patula permanent sample plot data from Kenya. In this dataset, trees were correctly numbered and identified but measurement interval varied from 1 to 13 years. Two simple regression approaches were used and compared to the optimization-based model recovery approach. Results： The optimization-based approach resulted in far more accurate simulations of stand basal area and number of surviving trees than the equations fitted through regression analysis. Conclusions： The optimization-based modelling approach can be recommended for growth modelling when the modelling data have been collected at irregular measurement intervals.     

Natural regeneration of oriental beech(Fagus orientalis Lipsky)trees in canopy gaps and under closed canopy in a forest in northern Iran

For developing nature-based silvicultural practices in a beech forest to promote, abundance, height,vitality, and preferred growth form, regenerated trees growing in gaps were compared with those under closed canopies.A systematic 50×50 m grid was plotted in a beech stand in the Kheyrud Experimental Forest for selecting trees to measure variables in gaps and under closed canopies.Abundance and mean height of regenerated beech trees were significantly higher in closed canopies than in canopy gaps.Beech seedlings with excurrent growth were significantly taller within regeneration patches under closed canopy.Moreover, regenerated trees with high vitality were more abundant in closed canopy areas than in gaps.Thus, beech regeneration should improve under closed canopies; hence, gaps in a near natural forest should be created only after adequate regeneration and appropriate growth under the parent tree in a closed canopy area is ensured.The results of this research have profound implications for the sustainable management of the forest and for ensuring sustainable beech regeneration.The presence of a closed canopy cover likely will reduce potential stresses on oriental beech regeneration.     

Using a stand-level model to predict light absorption in stands with vertically and horizontally heterogeneous canopies

Background： Forest ecosystem functioning is strongly influenced by the absorption of photosynthetically active radiation （APAR）, and therefore, accurate predictions of APAR are critical for many process-based forest growth models. The Lambert-Beer law can be applied to estimate APAR for simple homogeneous canopies composed of one layer, one species, and no canopy gaps. However, the vertical and horizontal structure of forest canopies is rarely homogeneous. Detailed tree-level models can account for this heterogeneity but these often have high input and computational demands and work on finer temporal and spatial resolutions than required by stand-level growth models. The aim of this study was to test a stand-level light absorption model that can estimate APAR by individual species in mixed-species and multi-layered stands with any degree of canopy openness including open-grown trees to closed canopies. Methods： The stand-level model was compared with a detailed tree-level model that has already been tested in mixed-species stands using empirical data. Both models were parameterised for five different forests, including a wide range of species compositions, species proportions, stand densities, crown architectures and canopy structures. Results： The stand-level model performed well in all stands except in the stand where extinction coefficients were unusually variable and it appears unlikely that APAR could be predicted in such stands using （tree- or stand-level） models that do not allow individuals of a given species to have different extinction coefficients, leaf-area density or analogous parameters. Conclusion： This model is parameterised with species-specific information about extinction coefficients and mean crown length, diameter, height and leaf area. It could be used to examine light dynamics in complex canopies and in stand-level growth models.     

GROWTH AND YIELD MODELS FOR DAHURIAN LARCH PLANTATIONS

Growth and yield models were developed for individual tress and stands based on336 temporary plots with 405 stem analysis trees of dahurian larch(Larix gmelinii(Rupr.)Rupr.)plantations throughout Daxing’anling mountains.Several equations were selected using nonlinearregression analysis.Results showed that the Richards equation was the best model for estimatingtree height,stand mean helght and stand dominant height from age; The Power equation was thebest model for prediction tree volume from DBH and tree height; The logarithmic stand volumeequation was good for predicting stand volume from age,mean height,basal area and other standvariables.These models can be used to construct the volume table, the site index table and other for-estry tables for dahurian larch plantations.     

Distribution of stem decay in the beech trees of the Azerbaijan and its impact on the output of commercial wood

To determine the distribution of stem decay in the beech stands of Azerbaijan, we sought to identify the species, number, and height of attachment of fruiting bodies;the extent of decay in tree trunks growing under different conditions;and its influence on the trees’ commercial wood. The research was conducted on three farms representing the most common forest types of the Greater Caucasus within Azerbaijan. Examination of the presence of fruiting bodies in the tree trunk revealed that stem decay is the most common infection in beech (Fagus orientalis) stands, especially in fresh, moist areas, with less infection under dry growing conditions. In this work, the length, diameter, and volume of decay were studied by infecting the trunks of 93 model trees affected with mushrooms in 1–4 m cuttings. Our results showed that as the age of the stand increased, extent, diameter, and volume of decay increased significantly: the extent of decay from 1.47 to 6.43 m;the diameter of the decay from 8.15 to 32.7 cm;and the volume of decay from 2.5 to 13.2%. The relationship between age and the specified indicators is presented graphically. Using data obtained from the same sample of trees, we determined the expected and actual yield of commercial wood by age class. We determined that stem decay in beech stands leads to a decrease in the yield of commercial wood on average from 25.1% in the middle-aged to 14.8% in overmature plantations, respectively, with an estimated yield of 40.8–62.7%. Here we present mathematical models of the output of commercial wood from the infected part of the stands by age classes with the use of average data on the extent of decay in model trees.     

Biomass production of hybrid aspen growing on former farm land in Sweden

We construct dry weight equations for hybrid aspen growing on former farmland in Sweden. Dry weight equations for fractions of hybrid aspen trees were also made. We estimated biomass production in 24 stands. The stands were located in Sweden at latitudes ranging from 55 to 60o N. The mean age was 18 years (range 15-23), the mean stand density 1090 stems·ha-1 (range 378 2374), and the mean diameter at breast height (over bark) 178 mm (range 85 244 mm). Soil types in the hybrid aspen stands were mainly clay (21 stands), tills (2 stands) and other (1 stand). The mean total standing dry weight above stump level (≈ 200 mm) for the hybrid aspen stands was 135±53 t·ha-1 with a range of 42 219 t·ha-1 . In addition to estimating conventional dry weights of trees and tree components, basic density, specific leaf area (SLA), projected leaf area (PLA) and leaf area index (LAI) were estimated and were in agreement with published figures.     

A management planning system for even-aged and uneven-aged forests in northeast China

The most common scientific approach to numerical landscape-level forest management planning is combinatorial optimization aimed at finding the optimal combination of the treatment alternatives of stands. The selected combination of treatments depends on the conditions of the forest, and the objectives of the forest landowners. A two-step procedure is commonly used to derive the plan. First, treatment alternatives are generated for the stands using an automated simulation tool. Second,the optimal combination of the simulated treatment schedules is found by using mathematical programming or various heuristics. Simulation of treatment schedules requires models for stand dynamics and volume for all important tree species and stand types present in the forest.A forest planning system was described for Northeast China. The necessary models for stand dynamics and tree volume were presented for the main tree species of the region. The developed models were integrated into the simulation tool of the planning system. The simulation and the optimization tools of the planning system were described. The optimization tool was used with heuristic methods, making it possible to easily solve also spatial forest planning problems, for instance aggregate cuttings.Finally, the use of the system is illustrated with a case study, in which nonspatial and spatial management plans are developed for the Mengjiagang Forest District.     

Estimating Pinus palustris tree diameter and stem volume from tree height,crown area and stand-level parameters

Accurate and efficient estimation of forest growth and live biomass is a critical element in assessing potential responses to forest management and environmental change. The objective of this study was to develop models to predict longleaf pine tree diameter at breast height （dbh） and merchantable stem volume （V） using data obtained from field measurements. We used longleaf pine tree data from 3,376 planted trees on 127 permanent plots located in the U.S. Gulf Coastal Plain region to fit equations to predict dbh and V as functions of tree height （H） and crown area （CA）. Prediction of dbh as a function of H improved when CA was added as an additional independent variable. Similarly, predic- tions of V based on H improved when CA was included. Incorporation of additional stand variables such as age, site index, dominant height, and stand density were also evaluated but resulted in only small improvements in model performance. For model testing we used data from planted and naturally-regenerated trees located inside and outside the geographic area used for model fitting. Our results suggest that the models are a robust alternative for dbh and V estimations when H and CA are known on planted stands with potential for naturally-regenerated stands, across a wide range of ages. We discuss the importance of these models for use with metrics derived from remote sensing data.     

Estimating canopy closure density and above-ground tree biomass using partial least square methods in Chinese boreal forests

Boreal forests play an important role in global environment systems. Understanding boreal forest ecosystem structure and function requires accurate monitoring and estimating of forest canopy and biomass. We used partial least square regression (PLSR) models to relate forest parameters, i.e. canopy closure density and above ground tree biomass, to Landsat ETM+ data. The established models were optimized according to the variable importance for projection (VIP) criterion and the bootstrap method, and their performance was compared using several statistical indices. All variables selected by the VIP criterion passed the bootstrap test (p<0.05). The simplified models without insignificant variables (VIP <1) performed as well as the full model but with less computation time. The relative root mean square error (RMSE%) was 29% for canopy closure density, and 58% for above-ground tree biomass. We conclude that PLSR can be an effective method for estimating canopy closure density and above-ground biomass.     

Aboveground biomass allometric equations and distribution of carbon stocks of the African oak(Afzelia africana Sm.)in Burkina Faso

The significant role of tropical forest ecosystems in the global carbon budget has increased the need for accurate estimates of tropical forest biomass. The lack of large-scale biomass allometric equations hampers the understanding of the spatial distribution of tree biomass and carbon stocks and their influencing factors in West Africa. This study aimed to develop allometric equations to estimate aboveground biomass of African oak(Afzelia africana Sm.) in Burkina Faso and to analyze factors affecting the variability of tree biomass and carbon storage.Sixty individual trees were destructively sampled in four protected areas along two climatic zones. In each climatic zone, log–log models were tested and fitted to each aboveground biomass component and to the totalaboveground biomass. Carbon content in tree aboveground components was evaluated using the ash method. All validated equations showed good fit and performance with high explained variance. Allometric equations differed between the Sudano-sahelian zone and the Sudanian zone,except for leaf biomass equations. Both biomass allocation and carbon content varied significantly between tree components but not between climatic zones. Carbon content in tree components followed the patterns of biomass allocation with branches accounting for the highest proportion. In the two climatic zones, carbon contents were50.18–52.62% for leaves, 54.78–54.94% for stems and54.96–55.99% for branches. Dry biomass ranged from509.05 to 765.56 kg tree~(-1) at site level and from 620.21 to624.48 kg tree~(-1) along climatic zones. Carbon content varied from 53.90% in the Sudano-sahelian zone to 54.39%in the Sudanian zone. This study indicated that climate does not influence aboveground biomass production and carbon sequestration of Afzelia africana along the Sudanosahelian and the Sudanian climatic zones of Burkina Faso.Future studies on climate–growth relationships should contribute to better understanding climate effects on biomass production and carbon storage.     

Stem taper equations for poplars growing on farmland in Sweden

We developed a simple polynomial taper equation for poplars growing on former farmland in Sweden and also evaluated the performance of some well-known taper equations. In Sweden there is an increasing interest in the use of poplar. Effective management of poplar plantations for high yield production would be facilitated by taper equations providing better predictions of stem volume than currently available equations. In the study a polynomial stem taper equation with five parameters was established for individual poplar trees growing on former farmland. The outputs of the polynomial taper equation were compared with five published equations. Data for fitting the equations were collected from 69 poplar trees growing at 37 stands in central and southern Sweden (lat. 55-60° N). The mean age of the stands was 21 years (range 14-43), the mean density 984 stems ha -1 (198 3,493), and the mean diameter at breast height (outside bark) 25 cm (range 12-40). To verify the tested equations, performance of accuracy and precision diameter predictions at seven points along the stem was closely analyzed. Statistics used for evaluation of the equations indicated that the variable exponent taper equation presented by Kozak (1988) performed best and can be recommended. The stem taper equation by Kozak (1988) recommended in the study is likely to be beneficial for optimising the efficiency and profitability of poplar plantation management. The constructed polynomial equation and the segmented equation presented by Max & Burkhart (1976) were second and third ranked. Due to the statistical complexity of Kozak’s equation, the constructed polynomial equation is alternatively recommended when a simple model is requested and larger bias is accepted.     

Residual tree damage along skidding trails in beech stands in Greece

We studied the damage caused to unfelled trees during skidding operations in four beech stands of northern and central Greece that were managed under differing harvesting systems.After timber was harvested we recorded and analyzed all damage to a width of 2 m along both sides of the skid trails.The percentage of damaged residual trees was 17–28 %.Higher numbers of saplings were uprooted or destroyed in parts of the stands with high natural regeneration.Most damaged trees suffered 1.33–1.90 wounds that were inflicted up to a height of 1 m above ground level.At all sites mean wound sizes were large,89–1190 cm2,and caused elevated risk of future fungal infection.The damage caused by skidding during timber harvesting can be minimized by better planning the harvest operations,and training forest workers in reduced impact logging.     

Linking individual-tree and whole-stand models for forest growth and yield prediction

Background： Different types of growth and yield models provide essential information for making informed decisions on how to manage forests. Whole-stand models often provide well-behaved outputs at the stand level, but lack information on stand structures. Detailed information from individual-tree models and size-class models typically suffers from accumulation of errors. The disaggregation method, in assuming that predictions from a whole-stand model are reliable, partitions these outputs to individual trees. On the other hand, the combination method seeks to improve stand-level predictions from both whole-stand and individual-tree models by combining them. Methods： Data from 100 plots randomly selected from the Southwicte Seed Source Study of Ioblolly pine （Pinus taedo L） were used to evaluate the unadjusted individual-tree model against the disaggregation and combination methods. Results： Compared to the whole-stand model, the combination method did not show improvements in predicting stand attributes in this study. The combination method also did not perform as well as the disaggregation method in tree-level predictions. The disaggregation method provided the best predictions of tree- and stand-level survival and growth. Conclusions： The disaggregation approach provides a link between individual-tree models and whole-stand models, and should be considered as a better alternative to the unadjusted tree model.     

Reconstructing the size of individual trees using log data from cut-to-length harvesters in Pinus radiata plantations: a case study in NSW,Australia

With their widespread utilization, cut-to-length harvesters have become a major source of ‘‘big data' for forest management as they constantly capture, and provide a daily flow of, information on log production and assortment over large operational areas. Harvester data afford the calculation of the total log length between the stump and the last cut but not the total height of trees. They also contain the length and end diameters of individual logs but not always the diameter at breast height overbark(DBHOB) of harvested stems largely because of time lapse, operating and processing issues and other system deficiencies. Even when DBHOB is extracted from harvester data, errors and/or bias of the machine measurements due to the variation in the stump height of harvested stems from that specified for the harvester head prior to harvesting and diameter measurement errors may need to be corrected. This study developed(1) a system of equations for estimating DBHOB of trees from diameter overbark(DOB) measured by a harvester head at any height up to 3 m above ground level and(2) an equation to predict the total height of harvested stems in P. radiata plantations from harvester data. To generate the data required for this purpose, cut-to-length simulations of more than 3000 trees with detailed taper measurements were carried out in the computer using the cutting patterns extracted from the harvester data and stump height survey data from clearfall operations. The equation predicted total tree height from DBHOB, total log length and the small end diameter of the top log. Prediction accuracy for total tree height was evaluated both globally over the entire data space and locally within partitioned subspaces through benchmarking statistics. These statistics were better than that of the conventional height-diameter equations for P. radiata found in the literature, even when they incorporated stand age and the average height and diameter of dominant trees in the stand as predictors. So this equation when used with harvester data would outperform the conventional equations in tree height prediction. Tree and stand reconstructions of the harvested forest is the necessary first step to provide the essential link of harvester data to conventional inventory, remote sensing imagery and Li DAR data. The equations developed in this study will provide such a linkage for the most effective combined use of harvester data in predicting the attributes of individual trees, stands and forests, and product recovery for the management and planning of P. radiata plantations in New South Wales, Australia.     

Aboveground biomass and nutrient allocation in an age-sequence of <Emphasis Type="Italic">Larix olgensis</Emphasis> plantations

Biomass and nutrient (N, P, K, Ca, Mg) stock in various aboveground tree components (stemwood, stembark, branches and leaves) were quantified in an age sequence of pure Larix olgensis planta- tions (20, 35, 53 and 69 years old) in Northeast China. The results show that the aboveground biomass allocation in various tree components was in the order of stemwood (62%-83%), branches (9%-21%), stembark (7%-11%) and leaves (1%-6%) for all stands. The proportion of stemwood biomass to total aboveground biomass increased whereas that of other tree components decreased consistently with stand age from 20 to 53 years old, but kept relatively constant with stand age from 53 and 69 years old. The nutrient allocation in various tree components generally followed the same pattern as the biomass allocation (i.e. stemwood > branches > stembark > leaves). The proportion of nutrient stock in leaves to total aboveground nutrient stock decreased consistently with increasing stand age, while that in stemwood increased with stand age from 20 to 53 years old but then decreased from 53 to 69 years old. The rate of nutrient removal for stands was estimated at different stand ages under different logging schemes, showing that the rate of nutrient removal would be unchanged when the rotation length was shortened to 20 years by the harvest of stem only, but greatly increased by the harvest of total aboveground biomass. The rate of nutrient removal would be a considerable reduction for all elements by debarking, especially for Ca.     

Individual-tree diameter growth model for Korean pine plantations based on optimized interpolation of meteorological variables

To explore the influence of meteorological variables on the growth of Korean pine(Pinus koraiensis Sieb.et Zucc.) plantations and provide a scientific reference for the production and management of Korean pine,three approaches to interpolate meteorological variables during the growing season(i.e.,May-September) were compared in Heilongjiang Province,China.Optimized meteorological variable interpolation results were then combined with stand and individual tree variables,based on data from 56 sample plots and 2886 sample trees from Korean pine plantations in two regions of the province to develop an individualtree diameter growth model(Model I) and an individualtree diameter growth model with meteorological variables(Model Ⅱ) using a stepwise regression method.Moreover,an individual-tree diameter growth model with regional effects(Model Ⅲ) was developed using dummy variables in the regression,and the significance of introducing these dummy variables was verified with an F-test statistical analysis.The models were validated using an independent data set,and the predictive performance of the three models was assessed via the adjusted coefficient of determination(R2) and root mean square error(RMSE).The results suggest that the growth increment in tree diameter of Korean pine plantations was significantly correlated with the natural logarithm of initial diameter(ln D),stand basal area(BAS),logarithmic deformation of the stand density index(ln SDI),ratio of basal area of trees larger than the subject tree to their initial diameter at breast height(DBH)(BAL/D),and the maximum growingseason precipitation(Pgmax).The individual-tree diameter growth models of Korean pine plantations developed in this study will provide a good basis for estimating and predicting growth increments of Korean pine forests over larger areas.     

Comparing the model forms estimating generalised diameter-height relationships in Tecomella undulata plantations in hot arid region of India

Four generalised diameter-height equations were developed and compared for pure and even-aged stands of Tecomella undulata in hot arid region of Rajasthan State in India. The data used to fit the equations consisted of 1 540 diameter-height observations collected from the plots laid out in uniformly stocked stands of varying age and density. The performance of four equations was tested by non-linear least squares regression and evaluated using different statistical criteria. Finally, these equations, with the same values of coefficients ob- tained during the fitting phase, were validated by an independent data set consisting of 854 diameter-height observations. Overall, equation （4） （Hui and Gadow function） was found to perform best for both the fitting data set as well as validation data set.     

Spatial correlation of pit and mound topography with canopy gaps in a virgin mixed beech forest,northern Iran

In a reserved forest parcel in a virgin eastern Hyrcanian mixed beech forest,80 ha was surveyed to determine the pit and mound topography,canopy gaps and dead trees.The aim was to investigate the spatial patterns and correlation of pit and mound features with canopy gaps.Seventy-five canopy gaps and 61 pit and mound features were identified.The univariate first order nearest neighbor(R_CE)and bivariate second order test(Ripley’s K)statistic were applied.R_CE statistics highlighted a general aggregation pattern for canopy gaps and pits and mounds,while pits and mounds alone were more clumped.Distances between canopy gaps were 130 m average,whereas distances between pit and mound features and dead trees were 60 and 78 m,respectively.Spatial positive correlation of canopy gaps with pits and mounds were observed with all distances.The result of spatial correlations between canopy gaps with pits and mounds confirmed that windthrows cause micro successions in fallen tree ecosystem-scale correlated with gap phase dynamics in the forest community-scale.     

Estimating oak forest parameters in the western mountains of Iran using satellite-based vegetation indices

Remote sensing is an important tool for studying and modeling forest stands.Vegetation indices obtained from Landsat-8 remotely sensed data were used to estimate the forest parameters in the western mountains of Iran.Thirtyfour sample points were selected on the map of Bayangan County,Kermanshah province,Iran.At each point,a cluster of five rectangular plots of 8100 m2 and 200 m apart was established.Some clusters were primarily sampled to determine the variance of the forest parameters.The coefficient of variation was used as a criterion for sample allocation.Stand density,canopy cover and basal area per hectare were calculated for each plot.Vegetation indices were extracted fromthe Landsat-8 images for each plot.Simple linear and nonlinear regressions were conducted to develop the models.The models were validated using an independent data set.Stability of model parameters was statistically evaluated.The results showed that Normalized difference vegetation index(NDVI)and Transformed normalized difference vegetation index(TNDVI)followed by Simple ratio vegetation index(SRVI)were the best predictors,explaining up to 91%of the variations with high precision.For NDVI,Soil adjusted vegetation index 2(SAVI2)and SRVI,the cubic model was more appropriate than the linear model for predicting the forest parameters.For this model,the R-square value increased while NRMSE decreased significantly.For Infrared percentage vegetation index(IPVI),the quadratic model was better,but,for other vegetation indices,nonlinear models were not superior to linear ones.Finally,it can be concluded that Landsat-8 imagery is suitable for predicting forest parameters in the oak forests of western Iran.Of course,large plots must be selected,and pre-classification is necessary to gain accurate and precise estimations.     

Parasitic plant in natural Boswellia papyrifera stands at Humera,Northern Ethiopia

In Boswellia papyrifera （Del.） Hochst natural stands, we stud- ied the association of parasitic plants with B. papyrifera trees from which frankincense was tapped and marketed for domestic and export markets. Data on the rate of infection of parasitic plants on B. papyrifera was collected in three transects located at separate locations around Baha kar, northern Ethiopia. Each transect had ten circular sample plots of 400 m2 and separated by 100 m. Species composition, DBH, height, crown di- ameter, number of main, secondary and tertiary branches and number of parasitic plants on individual trees were recorded. Sixteen tree species were recorded in the combined sample plots. The parasitic plant associ- ated with B. papyrifera was identified as Tapinanthus globiferus. This parasite infected 38% of Boswellia trees in sample plots. The infection rate of the parasitic plant varied from 1 to 33 per Boswellia tree. The infection of T. globiferus on B. papyrifera was predominantly limited to tertiary small branchlets arising from secondary branches; parasitic plants were absent on thick main and secondary branches. In all plots, infectionof T. globiferus was exclusively limited to Boswellia trees. The influence of T. globiferus parasitism on growth of Boswellia trees and its influence on yield of incense production needs further investigation. Management of natural stands for frankincense production should include measures to reduce infection by T. globiferus.