A Nonlinear Mixed-Effects Height-Diameter Model with Interaction Effects of Stand Density and Site Index for Larix olgensis in Northeast China

Zhang, Xiaofang; Fu, Liyong; Sharma, Ram P.; He, Xiao; Zhang, Huiru; Feng, Linyan; Zhou, Zeyu

doi:10.3390/f12111460

Cited by 10 publications

(12 citation statements)

References 38 publications

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“…In addition, the developed set of models significantly simplifies methods of growing stock volume estimation during sample-based forest inventory, since there is no need to measure heights of all tally trees on sample plots. Accordingly, the value of the variable h in the stem volume models (Table 3) can be estimated using equations (2)(3)(4)(5)(6).…”

Section: Resultsmentioning

confidence: 99%

“…The obtained data were summarised for each tree species and the average values of relative heights were calculated for all diameter classes observed in the study material. Equations (2)(3)(4) were used as mathematical models to characterize the h-d relationships. In particular, for pine, spruce, oak, beech, and ash, the following equation was used:…”

Section: Modelling H-d Relationshipsmentioning

confidence: 99%

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Height-diameter relationships and stem volume equations in young and middle-aged forest stands of Ukraine

Myroniuk¹,

Svynchuk²,

Bilous³

et al. 2022

Ukr. j. for. wood sci.

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Height-diameter (h-d) relationships in forest stands are commonly used in various scientific and practical forestry applications. Accurate h-d models combined with tree stem volume equations are recognised to be effective in growing stock volume estimation. The purpose of the study was threefold: 1) development of a set of mathematical models of the h-d relationship in young and middle-aged forest stands for ten forest-forming species in Ukraine; 2) modelling stem volume in above mentioned forest stands; 3) comparison of established mathematical models with corresponding ones for premature, mature, and overmature forest stands. The study was based on permanent and temporal sample plots data (about 600) established in forest stands during 1950s-2020s within the most forested regions of Ukraine (Polissia, Forest-Steppe, Carpathians). In total, about 10,000 sample trees were measured on the sample plots to accurately estimate their stem volume outside bark. The h-d models demonstrated very similar relationships between stem heights and diameters for most of our species except for spruce and fir in mountain Carpathian forests where the steeper h-d curves were obtained. The study revealed that birch and hornbeam tree stems had the lowest volumes among surveyed species. The results also indicated that tree species tend to have higher volumes (up to 7% for coniferous, and up 10% for aspen and birch forests) in young and middle-aged forest sands than in older ones. For the other species, a statistically significant difference between stem volumes of trees of different ages was not observed. The developed mathematical models can complement the corresponding models for older groups of forest stands since they revealed an important aspect of relationships between the key tree stem parameters. These models are also applicable for a more precise stem volume estimation during thinning operations in the young and middle-aged forests in Ukraine

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Section: Resultsmentioning

confidence: 99%

Section: Modelling H-d Relationshipsmentioning

confidence: 99%

Height-diameter relationships and stem volume equations in young and middle-aged forest stands of Ukraine

Myroniuk¹,

Svynchuk²,

Bilous³

et al. 2022

Ukr. j. for. wood sci.

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“…It can also be viewed as a composite quantitative variable, a product of the interaction between the growth potential of the trees, speeding up the self-thinning process when high, and stand stocking. A study by Zhang et al (2021) revealed that the inclusion of the interaction effects of stand density and site index could significantly improve the prediction accuracy of the height-diameter model for Larix olgensis Henry. In addition, the modified Gaffrey's model derived here specifies the estimated tree height value according to the social status of the tree as well.…”

Section: Discussionmentioning

confidence: 99%

A Parsimonious Generalised Height-Diameter Model for Scots Pine Plantations in Bulgaria

Stankova

Dimitrova

Dimitrov

et al. 2022

SEEFOR

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Considering the state-of-the-art of forest inventory in Bulgaria, our investigation pursued development of a parsimonious generalised height-diameter model for the Scots pine plantations in the country. A number of 2-, 3- and 4-predictor candidate models were examined and compared based on their goodness-of-fit statistics. Data records obtained in variable-sized sample plots, established throughout the distribution range of the plantations and covering the variety of sites, densities and growth stages were used to fit the models. Two hundred twenty-four plot-level measurements and 3056 tree height-diameter pairs were utilised for parameterization. An independent data set of tree-level measurements and two sets of dominant height-diameter pairs, estimated for differently defined top height tree collectives, were used for model validation. Statistical analyses were carried out using packages nlstools, moments, equivalence, car, nlme, stats and the results were illustrated with ggplot2 and graphics packages of R software environment. A modified form of Gaffrey’s model was selected, which estimates the height of a tree through the breast-height tree diameter, mean stand height and diameter, and accounts for the tree social status. It was fitted by generalised non-linear least squares method, with residual variance weighted by a product of tree diameter and mean stand height exponential functions. An adjusted coefficient of determination of 0.917 and residual standard error of 0.794 m indicated the high predictive potential of the derived model. Validation tests showed that the estimated regression line is very well fitted to the independent data and is appropriate to forecast dominant stand heights. The range of errors, relative to the predicted dominant height values, was narrow, ±25-30%, with low magnitude of the average of their absolute values (4-5%). The equivalence tests rejected the null hypothesis of dissimilarity regarding model bias (observations-predictions line intercept) for all validation data sets, for a region of equivalence as narrow as ±5%. The 3-predictor generalised height-diameter model developed in our study needs information readily available from the inventories and therefore can be broadly used. Its application in dominant stand height prediction is recommended.

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“…The h-d relationship in even-and uneven-aged forest stands is also important issue [9]. Some recent publications indicate that h-d relationships of trees depend on the origin of forest stands [10] and are closely related to their density [11]. Site conditions directly impact the h-d relationships of trees [12].…”

Section: Bilous Et Almentioning

confidence: 99%

“…are usually considered as factors that introduce random variations in the h-d relationships in forest stands of the same age. While fixed-effect models characterise the most typical relationship for a wide group of forest stands, mixed-effect models explain the random component of covariance of these characteristics for a particular forest stand [11]. Such models, apart from fixed-effect terms of the equation (the typical stand), also contain random-effect terms that describes remove the differences between each individual forest stand in relation to the typical one, thus revealing specific patterns of heights and diameters depending on random factors.…”

Section: Bilous Et Almentioning

confidence: 99%

Stem volume by height classes of immature, mature and overmature stands of the main forest-forming species of Ukraine

Bilous¹,

Myroniuk²,

Svynchuk³

et al. 2022

Ukr. j. for. wood sci.

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Generally, it is impossible to measure diameters and heights of all trees in a forest stand. Therefore, models of relationships between heights (h) and diameters (d) of trees are commonly used in practice for stem volume estimation. This study aimed at developing models of tree height-diameter (h-d) relationships as well as corresponding models of the tree stem volume for immature, mature and overmature stands of the main forest-forming species of Ukraine. This paper is a aggregation of long-term studies of the stem volume, which are based on the results of measuring about 10 thousand sample trees. Modelling of the tree height-diameter relationships was performed using relative height values. The methodology used in this study allowed generalising the measurements of sample trees collected in stands of various forest site types, productivity levels, and age categories. The average height of trees with a diameter of 24 cm was taken as the reference during modelling relative heights, while the diameter of 40 cm was chosen as the reference for overmature Scots pine stands. As a result, the parameters of a unified mathematical model of relative heights for immature, mature, and overmature stands of the main forest-forming tree species of Ukraine were established. Based on these models, height-diameter relationships in forest stands of different height classes were predicted. The authors demonstrated that the developed mathematical models substantially simplify the methodology of field work during timber surveys. The paper also presents models of the tree stem volume. These models predict the stem volume outside the bark based on diameters and heights of trees or using the developed models of h-d relationships. In this study, a unified system of mathematical models of stem volume by height classes were created for immature, mature, and overmature stands of the main forest-forming species of Ukraine. The results of the study are introduced to the National Forest Inventory of Ukraine for growing stock volume calculation at sample plot level using measurements of individual trees. The developed models can be used both by operation forestry (estimation of the timber volume during harvesting), and forest management (forecasting the future structure of forests and estimating the growing stock volume), as well as in the forest ecology

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A Nonlinear Mixed-Effects Height-Diameter Model with Interaction Effects of Stand Density and Site Index for Larix olgensis in Northeast China

Cited by 10 publications

References 38 publications

Height-diameter relationships and stem volume equations in young and middle-aged forest stands of Ukraine

Height-diameter relationships and stem volume equations in young and middle-aged forest stands of Ukraine

A Parsimonious Generalised Height-Diameter Model for Scots Pine Plantations in Bulgaria

Stem volume by height classes of immature, mature and overmature stands of the main forest-forming species of Ukraine

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