Stand volume functions for picea abies in western Norway

A material of 1156 observations was used to develop two Norway spruce (P. abies (L.) Karst.) stand volume functions for western Norway. An additive model initially based on a polynomial of second degree was found to be most suitable. The independent variables were stand basal area, Lorey's mean height, the product of basal area and mean height, and the square of the mean height.

In order to roughly reflect the different climatical conditions within western Norway, all municipalities were classified into the categories “inland” and “coast”. The individual observations were assigned the category of the municipality in which they were sited. The type of district was included in the selected additive model by means of a dummy variable approach. Testing showed that two individual regressions should be recommended for prediction purposes in the respective districts. R² was 0.998 and C.V. was less than 2.5%. The regressions fitted most parts of the material very well, with exception for low densities for inland districts. Testing by means of an independent data set indicated no systematic differences.     

基于多水平非线性混合效应蒙古栎林单木断面积模型

以吉林省汪清林业局184块样地中的10 111株蒙古栎为例,首先选用线性函数、Richards函数、Logistic 函数、指数函数等7种常用函数形式,分析4个因变量(后期胸径、后期胸高断面积、直径增量和胸高断面积增量)与前期胸径的影响,确定一个用于构建混合效应模型的基础模型。然后确定同时考虑林场效应和林场与样地交互效应时基础模型中最优的形式参数构造形式,利用逐步回归方法确定模型中所包含的林分变量,并分析和比较用来消除异方差的3种常用残差方差函数(指数函数、幂函数和常数加幂函数),最后检验模型预测效果。结果表明:Wykoff模型且因变量为后期胸高断面积拟合效果较好,故作为基础模型;除前期胸高直径(D)外,当考虑坡度正切(ST),对象木胸高直径与样地算术平均直径的比(RAD),样地胸高总断面积(TBA),样地中大于对象木直径所有树木的胸高断面积和(GSBA),对象木胸高断面积与样地算术平均胸高断面积的比 (RABA)和对象木胸高断面积与样地胸高总断面积的比(RBA)等林分变量时能进一步提高模型预测精度;对于残差方差,指数函数、幂函数和常数加幂函数都能消除异方差,但幂函数效果最好;当模型同时考虑林场效应和林场与样地交互效应时预测精度最高。     

Das Wachstum von Pinus pinaster (Aiton) in Abhängigkeit vom Standraum

Summary Spacing trials were established inPinus pinaster, in plantations in the Southern and South-Western Cape Province in South Africa. Eight spacings, with nominal initial stem numbers between 125 and 3000 were tested in each of the two trials, with a single replicate in each experiment. The Chapman-Richards growth model was applied to mean diameter, mean height and basal area/ha. For diameter and height, the assumption m=0 holds true, but for basal area/ha, this parameter is related to initial stem number. The volume growth of each sample plot was estimated from equations with basal area and mean height and their interaction as predictor-variables. The regression model also included constraints for basal area and height, to prevent anomalies for the estimated volume per hectare at young age. Each of the trials contained a number of plots, thinned after the onset of competition. The growth rates in these plots was statistically significantly greater than that of the same stand density in the unthinned plots.      

Possibilities for Harvester-based Forest Inventory in Thinnings

This study investigated the possible estimation of forest characteristics using the information collected by the harvester in first thinnings. For the analysis a complete forest inventory was carried out in a stand, which was subsequently thinned. The global mean values of tree diameter, tree height, basal area and stem density were estimated, and further, a spatial analysis was carried out to investigate whether the data collected by the harvester could be used to generate a continuous spatial model of the forest. The results indicated that the global mean diameter and height may be estimated, whereas area-related properties, such as basal area and stem density, are more difficult to estimate. The spatial distribution of the diameter and height remained similar after the thinning, whereas the basal area and stem density had become more homogeneous after the thinning. From the trees removed in the thinning a continuous spatial model of tree diameter was developed. It reproduced the spatial structure of the original trees to some extent ( R 2 = 0.27, RMSE = 14.3 mm).     

Estimating percentile-based diameter distributions in uneven-sized Norway spruce stands using airborne laser scanner data

Abstract

A model for prediction of stand basal area and diameters at 10 percentiles of a basal area distribution was estimated from small-footprint laser scanner data from primeval conifer forest using partial least squares regression. The regression explained 44–80% and 67% of the variability of the 10 percentiles and stand basal area, respectively. The predicted percentiles, scaled by the predicted stand basal area, were used to compute diameter distributions. A cross-validation showed that the mean differences between the predicted and observed number of stems by diameter class were non-significant (p>0.05) for 22 of 29 diameter classes. Moreover, plot volume was calculated from the predicted diameter distribution and cross-validation revealed a non-significant deviation between predicted and observed volume of ?3.3% (of observed volume). An independent validation showed non-significant mean differences for 20 of 21 diameter classes for data corresponding to the model calibration data. Plot volumes calculated from the predicted diameter distributions deviated from observed volume by ?4.4%. The model reproduced diameter distributions corresponding to the model calibration data (uneven-sized forest) well. However, the model is not flexible enough to reproduce normal and uniform diameter distributions. Volume estimates derived from predicted diameter distributions were generally well determined, irrespective of the observed distribution.     

自动调控树高曲线和一元立木材积模型*

吉林延边地区目前年用一元立木材积表的误差，主要来源于估计各径阶高的误差。本文以双曲线为例，介绍三种多元树高曲线模型；称为自动调控树高曲线。在测定小班（或样地）直径分布时，同时测定小班（或样地）的断面积平均高，由此计算树高曲线，进而得到相应的一元立木材积表。其首选自动调控树高曲线式：Ｈ＝Ｈｍ．Ｄ／［Ｄ＋（Ｈｍ／Ｈｇ－１）Ｄｇ］。此式导出的一元材积表，经验证与实测材积的误差比原地区一元材积表减少约５０     

Determination of mean diameter by basal area in stands of picea abies and pinus sylvestris in southeastern Norway by means of aerial photographs

Mean diameter by basal area (d_g) is an important stand variable for long‐term economic forecasts of forest holdings. In order to use stand‐by‐stand surveys based on aerial photo interpretation as the data basis for forecasts, d_g has to be determined. The objective was to develop and test a regression function for d_g in mature stands of Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) applicable in southeastern Norway. A study of 700 plots was used to estimate a function for d_g . An additive model was found to be most suitable. The independent variables were potential yield capacity, Lorey's mean tree height, crown closure determined by ocular estimation by means of aerial photographs, and the product of potential yield capacity and crown closure. The R² value was 0.604 and the coefficient of variation was 10.8%. The regression fitted most parts of the calibration data quite well, but it may overestimate the mean diameter in pure spruce stands by 1–2%, and underestimate the diameter in pure pine stands by 3%. For mixed coniferous stands the regression seems satisfactory. Testing by means of an independent data set showed systematic errors of 3–23%. The systematic errors were due partly to calibration problems in connection with the ocular crown closure estimation.     

Spacing effects in an unthinned 11-year-old Terminalia superba plantation in the dry lowland rainforest area of Nigeria

Data from a spacing study in an 11-year-old plantation of Terminalia superba were examined with response models. Analysis of variance of the latin-square design with four spacings indicated significant effects of spacing on survival and mean diameter, as well as basal area, height and volume growth. Response model analysis showed that a planting density of 2391 trees ha⁻¹ maximizes basal area growth and 2331 trees ha⁻¹ maximizes volume growth, but the largest mean diameter is produced by planting 232 trees ha⁻¹. Guides are provided for the forest manager's use in determining trade-offs between maximum timber production and space between trees to grow agricultural crops within the Taungya system.     

Forest variable estimation using photogrammetric matching of digital aerial images in combination with a high-resolution DEM

Abstract

The rapid development in aerial digital cameras in combination with the increased availability of high-resolution Digital Elevation Models (DEMs) provides a renaissance for photogrammetry in forest management planning. Tree height, stem volume, and basal area were estimated for forest stands using canopy height, density, and texture metrics derived from photogrammetric matching of digital aerial images and a high-resolution DEM. The study was conducted at a coniferous hemi-boreal site in southern Sweden. Three different data-sets of digital aerial images were used to test the effects of flight altitude and stereo overlap on an area-based estimation of forest variables. Metrics were calculated for 344 field plots (10 m radius) from point cloud data and used in regression analysis. Stand level accuracy was evaluated using leave-one-out cross validation of 24 stands. For these stands the tree height ranged from 4.8 to 26.9 m (17.8 m mean), stem volume 13.3 to 455 m³ ha^?1 (250 m³ ha^?1 mean), and basal area from 4.1 to 42.9 m² ha^?1 (27.1 m² ha^?1 mean) with mean stand size of 2.8 ha. The results showed small differences in estimation accuracy of forest variables between the data-sets. The data-set of digital aerial images corresponding to the standard acquisition of the Swedish National Land Survey (Lantmäteriet), showed Root Mean Square Errors (in percent of the surveyed stand mean) of 8.8% for tree height, 13.1% for stem volume and 14.9% for basal area. The results imply that photogrammetric matching of digital aerial images has significant potential for operational use in forestry.     

基于树高和树冠因子的立木材积模型研究

[目的]由于激光雷达技术已经能准确测定立木树高及相关树冠因子,应用该技术建立基于树高和树冠因子的立木材积模型,为激光技术在森林蓄积估计中提供技术支撑.[方法]利用云杉、冷杉、栎树、桦树4个树种组的3 010株实测样木数据,分析了立木材积与胸径、树高、树冠因子之间的相关关系;并通过对数回归方法构建了基于树高和树冠因子的立木材积模型,用确定系数R²和平均预估误差MPE等6项指标对模型进行评价.[结果]表明,立木材积与单一因子之间的相关,以胸径最为紧密,其次是树高,再次是冠长和冠幅.基于树高和树冠因子的立木材积模型中,以树高和冠幅作为解释变量的二元模型效果较好,再增加冠长因子的三元模型改进不大.云杉、冷杉、栎树、桦树4个树种组基于树高冠幅的立木材积模型,其R²分别为0.81、0.80、0.76和0.77,MPE分别为4.7%、5.3%、5.4%和5.3%,模型预估精度均能达到95%左右.[结论]本文对材积与林木因子之间相关关系的定量分析,建立了云杉、冷杉、栎树、桦树4个树种的立木材积模型,模型预估精度高.为激光雷达技术定量估测森林参数提供了依据.     

Thinning intensity and growth response in SW-European Scots pine stands

The effect of different thinning intensities on growth and yield was studied in Pinus sylvestris L. stands at the south-western limit of its distribution area (Central Spain), using five long-term thinning trials. Data were analysed collectively considering several factors (trial, block, plot and period) as random effects. Total volume and volume increment decreased with thinning intensity, this loss being more significant in the case of moderate and heavy thinning. No difference was found among treatments for total basal area or the increment in basal area. The results revealed an optimum basal area (Assmann’s definition) between 85 and 100% of the basal area in unthinned plots. Volume growth loss associated with heavy thinnings (reduction of 18% in volume increment) was smaller than that reported in Central and Northern European regions (greater than 25%). Height increment was not influenced by thinning, whereas dominant and quadratic mean diameter increments increased with the thinning intensity. The response of diameter growth to thinning was greater at younger ages (less than 50 y) and in medium-sized trees.     

Predicting Potential Density and Basal Area Development in the Social Forestry Plantations of Acacia nilotica in Gujarat State of India

ABSTRACT

Growth modelling is an important and effective tool for evaluating the effects of a particular management action on the future development of a forest ecosystem. However, such necessary growth models are not available for many indigenous tree species in India. Acacia nilotica is an important multipurpose tree species found in India and growth models are required for proper management of the species in the region. This paper presents equations for estimating potential stand density and predicting basal area in pure even-aged stands of A. nilotica in Gujarat State of India. Although no thinning was suggested, decrease in the number of trees in the stands was observed because of mortality due to overcrowding and some biotic factors. Relationships between quadratic mean diameter and stems per hectare were developed, which was used to establish the limiting density line. Eight different stand level models, belonging to the path invariant algebraic difference form of a non-linear growth function, were compared for projecting basal area. They can be used to predict future basal area as a function of stand variables like dominant height and stem number per hectare and are crucial for evaluating different silvicultural treatment options. The performance of the models was evaluated using different statistical criteria to recommend the suitable model for projecting the basal area in A. nilotica stands.     

Practical large-scale forest stand inventory using a small-footprint airborne scanning laser

Mean tree height, dominant height, mean diameter, stem number, basal area and timber volume of 116 georeferenced field sample plots were estimated from various canopy height and canopy density metrics derived by means of a small-footprint laser scanner over young and mature forest stands using regression analysis. The sample plots were distributed systematically throughout a 6500 ha study area, and the size of each plot was 232.9 m². Regressions for coniferous forest explained 60–97% of the variability in ground reference values of the six studied characteristics. A proposed practical two-phase procedure for prediction of corresponding characteristics of entire forest stands was tested. Fifty-seven test plots within the study area with a size of approximately 3740 m² each were divided into 232.9 m² regular grid cells. The six examined characteristics were predicted for each grid cell from the corresponding laser data using the estimated regression equations. Average values for each test plot were computed and compared with ground-based estimates measured over the entire plot. The bias and standard deviations of the differences between predicted and ground reference values (in parentheses) of mean height, dominant height, mean diameter, stem number, basal area and volume were ?0.58 to ?0.85 m (0.64–1.01 m), ?0.60 to ?0.99 m (0.67–0.84 m), 0.15–0.74 cm (1.33–2.42 cm), 34–108 ha^?1 (97–466 ha^?1), 0.43–2.51 m² ha^?1 (1.83–3.94 m² ha^?1) and 5.9–16.1 m³ ha^?1 (15.1–35.1 m³ ha^?1), respectively.     

Development of a stand density management diagram for even-aged pedunculate oak stands and its use in designing thinning schedules

Density management is the usual method used by silviculturiststo achieve a desired future stand condition, and one of themost effective methods of design, display and evaluation ofalternative density management regimes in even-aged stands isthe use of stand density management diagrams. In the presentstudy, we describe a method for developing thinning schedulesfor even-aged pedunculate oak (Quercus robur L.) stands in Galicia(north-western Spain), using a density management diagram. Thediagram integrates the relationships among stand density, dominantheight, quadratic mean diameter and stand volume in a singlegraph. The data used in its construction were obtained from172 sample plots located throughout Galicia. The diagram isbasically composed of two equations: the first relates the quadraticmean diameter to the stand density and dominant height; thesecond relates the stand volume to the quadratic mean diameter,stand density and dominant height. These equations were fittedsimultaneously using full information maximum likelihood. Therelative spacing index is used to characterize the growing stockand the diagram provides isolines for dominant height, numberof trees per hectare, quadratic mean diameter and stand volume.Dominant height isolines together with the site index curvesallow specification of the timing of thinnings while intermediateand final harvest volumes are calculated using the stand volumesisolines.     

Pre-commercial thinning effects on growth, yield and mortality in even-aged paper birch stands in British Columbia

The aim of this study was to quantify 5-year growth, yield and mortality responses of 9- to 13-year-old naturally regenerated, even-aged paper birch (Betula papyrifera Marsh.) stands to pre-commercial thinning in interior British Columbia. The study included four residual densities (9902–21,807 stems ha⁻¹ (unthinned control), 3000, 1000 and 400 stems ha⁻¹) and four sites with 3-fold within-site replication in a randomised block design. The largest, straightest, undamaged trees were selected to leave during thinning. Thinning reduced stand basal area from 5.90 m² ha⁻¹ in the control to 2.50, 1.53 and 0.85 m² ha⁻¹ in the three thinning treatments, representing 42, 26 and 15% of control basal area, respectively. After 5 years, total stand volume per plot remained lower in the three thinning treatments than the control (50.20, 30.07, 18.99 and 11.86 m³ in the control, 3000, 1000 and 400 stems ha⁻¹ treatments), whereas mean stand diameter, diameter increment, height, and height increment were increased by thinning, and top height (tallest 100 trees ha⁻¹) was unaffected. When a select group of crop trees (largest 250 trees ha⁻¹) in the thinning treatments was compared with the equivalent group in the control, there was a significant increase in mean diameter, diameter increment, basal area, basal area increment, and volume increment. Mean height, height increment, top height, and total volume were unaffected by thinning. Crop tree diameter increment was the greatest following thinning to 400 stems ha⁻¹ for all diameter classes. Thinning to 1000 stems ha⁻¹ resulted in lower diameter increment than thinning to 400 stems ha⁻¹ but tended to have higher volume increment. Dominant trees responded similarly to subdominant trees at 400 stems ha⁻¹, but showed the greatest response at 3000 stems ha⁻¹. Results suggest that pre-commercial thinning of 9–13-year-old stands to 1000 stems ha⁻¹ would improve growth of individual trees without seriously under-utilising site resources.     

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.     

一种与直径分布型无关的预测林分直径累积分布的方法

本文推导出一组联系林分平均直径生长和直径累积分布生长之间的方程式。根据这些方程建立的全林分生长模型和径阶模型或与距离无关的单木模型之间的关系，可以指导由林分断面积总生长向单木直径生长的分配。采用这一组方程，根据二个不同时间点上算术平均直径和均方平均直径回收生长模型和枯损模型中的参数，保证林分水平预测的结果和径级水平或单木水平预测的结果相容。采用一个误差函数来刻化相同直径林木在生长过程中的分化，证明了忽略这项误差函数可能导致预测的直径分布范围小于实际的范围。因此，加上一个误差函数预测直径分布在一定程度上提高了直径分布预测的精度。最后一个实例说明计算过程。     

A mixed nonlinear height–diameter model for pyrenean oak (Quercus pyrenaica Willd.)

A nonlinear mixed-effects modelling approach was used to model the individual tree height–diameter relationship in pyrenean oak (Quercus pyrenaica Willd.). A set of 24,627 pairs of height–diameter measurements were used to fit the model. These were taken at 950 Spanish National Forest Inventory plots embracing six different biogeoclimatic strata. Eleven biparametric nonlinear height–diameter equations were evaluated to find a local model, which only includes the dimensions of the tree as explanatory variables. After selecting the local model, a regional or generalized model was studied. The following stand variables were tested for inclusion in the model as fixed effects: stand density, quadratic mean diameter, arithmetic mean diameter, dominant diameter, arithmetic mean height, dominant height and basal area. Dominant height and basal area of the stand were found to produce the most satisfactory fits in the stand model. Interregional variability was studied by including strata effects as dummy categorical variables and was analysed using the non-linear extra sum of squares method and the Lakkis–Jones test. Height–diameter models were found to be similar for the six biogeoclimatic strata. Finally, a mixed nonlinear model technique was applied to fit the definitive model. By calibrating the model it is possible to predict random components of definitive model from height measurements previously taken from a subsample of trees. The different alternatives tested reveal that only two or three trees are necessary to calibrate the model.     

Using multi-source data to map and model the predisposition of forests to wind disturbance

Natural disturbances such as wind are known to cause threats to ecosystem services as well as sustainable forest ecosystem management. The objective of this research was to better understand and quantify drivers of predisposition to wind disturbance, and to model and map the probability of wind-induced forest disturbances (P_DIS) in order to support forest management planning. To accomplish this, we used open-access airborne light detection and ranging (LiDAR) data as well as multi-source National Forest Inventory (NFI) data to model P_DIS in southern Finland. A strong winter storm occurred in the study area in December 2011. High spatial resolution aerial images, acquired after the disturbance event, were used as reference data. Potential drivers associated with P_DIS were examined using a multivariate logistic regression model. The model based on LiDAR provided good agreement with detected areas susceptible to wind disturbance (73%); however, when LiDAR was combined with multi-source NFI data, the results were more promising: prediction accuracy increased to 81%. The strongest predictors in the model were mean canopy height, mean elevation, and stem volume of the main tree species (Norway spruce and Scots pine). Our results indicate that open-access LiDAR data can be used to model and map the probability of predisposition to wind disturbance, providing spatially detailed, valuable information for planning and mitigation purposes.