Height Increment Models Research Articles

Individual Tree Height Increment Model for Quercus mongolica Secondary Forest in the Northeastern China Using Generalized Nonlinear Two-Level Mixed-Effects Model

(1) Background: Mongolian oak secondary forest is widely distributed in the northeast of China, and most of these forests are formed after the overcutting of broad-leaved Pinus koraiensis mixed forest. Most of the forest productivity is low and the ecological function is degraded, due to insufficient understanding of Mongolian oak and lack of scientific management. Deepening the research on exploring reasonable management measures of Mongolian oak secondary forest to an improved stand status is the basis for improving its quality and promoting its forward succession process. (2) Methods: Twelve permanent plots with an area of 1 ha were established in the Mongolian oak secondary forest on Tazigou forest farm in Wangqing, Jilin Province of northeastern China. The response of tree height increment of Mongolian oak secondary forest is studied based on the survey data of 2013 and 2018. Two-level nonlinear mixed-effects models were constructed to predict the height of a single tree using sample plots and tree species as random effects, combined with a variety of tree size factors, site factors, and competitive factors as independent variables. (3) Results: The significant factors related to the height increment of Mongolian oak secondary forest are the initial diameter at breast height as the size of the tree itself (DBH), height (H), crown height ratio (CR), and site productivity index reflecting site quality (SPI). The distance-dependent and distance-independent competition indexes have no significant effect on tree height increment. The fitting accuracy of the two-level mixed-effects model that introduces plots and tree species as random effects has been greatly improved (coefficient of determination R2 increased by 51.8%). The prediction results show that the two trees with the largest DBH have the strongest prediction ability. (4) Conclusions: The generalized nonlinear two-level mixed-effects model constructed in this study can describe the height increment of an individual tree in the Mongolian oak secondary forest. Two sample trees, namely the two largest trees in each sub-plot, were applied for estimating the random effects when both measurement cost and potential errors of prediction were balanced.

Diameter, height and volume increment single tree models for improved Sitka spruce in Great Britain

Abstract The British forestry sector lacks reliable dynamic growth models for stands of improved Sitka spruce, the most important commercial forest type in Great Britain. The aim of this study is to fill this gap by trialling a new modelling framework and to lay the foundations of a future dynamic growth simulator for that forest type. First, we present single tree diameter and height increment models that are climate sensitive and include explicit competition effects. The predictions from the increment models are pooled to project diameter and height at a given age. These projections are then used as inputs to an integrated taper model from which stochastic tree volume predictions are obtained. Retrospective data from over 1400 trees collected in two extensive genetic trials in Scotland and Wales were used for the purposes of this study. Diameter increment and height increment predictions were highly accurate and diameter and height projections proved consistent. The predicted volume at the time of harvesting also exhibited a high degree of accuracy, which shows the robustness of our approach. Further data will be needed in the future to recalibrate the present models and extend their range of validity to the whole of Great Britain.

Tree Height Increment Models for National Forest Inventory Data in the Pacific Northwest, USA

The United States national inventory program measures a subset of tree heights in each plot in the Pacific Northwest. Unmeasured tree heights are predicted by adding the difference between modeled tree heights at two measurements to the height observed at the first measurement. This study compared different approaches for directly modeling 10-year height increment of red alder (RA) and ponderosa pine (PP) in Washington and Oregon using national inventory data from 2001–2015. In addition to the current approach, five models were implemented: nonlinear exponential, log-transformed linear, gamma, quasi-Poisson, and zero-inflated Poisson models using both tree-level (e.g., height, diameter at breast height, and compacted crown ratio) and plot-level (e.g., basal area, elevation, and slope) measurements as predictor variables. To account for negative height increment observations in the modeling process, a constant was added to shift all response values to greater than zero (log-transformed linear and gamma models), the negative increment was set to zero (quasi-Poisson and zero-inflated Poisson models), or a nonlinear model, which allows negative observations, was used. Random plot effects were included to account for the hierarchical data structure of the inventory data. Predictive model performance was examined through cross-validation. Among the implemented models, the gamma model performed best for both species, showing the smallest root mean square error (RSME) of 2.61 and 1.33 m for RA and PP, respectively (current method: RA—3.33 m, PP—1.40 m). Among the models that did not add the constant to the response, the quasi-Poisson model exhibited the smallest RMSE of 2.74 and 1.38 m for RA and PP, respectively. Our study showed that the prediction of tree height increment in Oregon and Washington can be improved by accounting for the negative and zero height increment values that are present in inventory data, and by including random plot effects in the models.

MOSES – A tree growth simulator for modelling stand response in Central Europe

Moses (MOdelling Stand rESponse) is a distance and potential-dependent single-tree growth simulator. It consists of a diameter and height increment model, a dynamic crown model and models that calculate mortality and regeneration. It was originally calibrated for spruce, beech and pine forests in Austria and has been recalibrated several times throughout the years. In this study, we recalibrated and validated the increment models and the mortality model within MOSES using the latest large and holistic dataset based on monitoring and permanent inventory plots for seven of the most common tree species in Europe (five for the mortality model). These plots were mainly from Austria and Switzerland, as well as Germany. In addition, we calibrated sets of coefficients for the “species groups” (i) other broadleaf and (ii) other conifer trees. The total dataset comprises 278,979 repeated tree measurements, 56,312 of them were used for calibration and 222,667 for validation. The validation of the newly parameterized growth and mortality models exhibit consistent and unbiased estimates for tree growth in central European forests using the MOSES simulator.

Resource communication. Individual-tree growth model for radiata pine plantations in northwestern Spain

Individual-tree basal area and height increment models were developed with data from 130 permanent plots of Pinus radiata D. Don located in Galicia (northwestern Spain). Mixed-models techniques were used for model fitting. Covariates acting at tree and stand level were included as fixed effects. Estimated values of stand variables obtained from aggregation of individual-tree predictions were used in model evaluation. The developed models accounted for 54% of the variability in basal area increment and 36% of the variability in height increment, with mean errors of 16 cm2 and 0.36 m, respectively. These models, along with an existing individual-tree mortality model, constitute a whole individual-tree growth model that can be used to simulate forest management alternatives, helping in forest managers’ decision making.

Compatible diameter and height increment models for lodgepole pine, trembling aspen, and white spruce

In this study, compatible height and diameter increment models were fitted for lodgepole pine ( Pinus contorta Dougl. ex Loud. var. latifolia Engelm.), trembling aspen ( Populus tremuloides Michx.), and white spruce ( Picea glauca (Moench) Voss), using the relationship between diameter and height growth. It was assumed that tree diameter increment is directly proportional to height increment, and the proportionality constant is a function of competition and site productivity. The results showed that the fit statistics are comparable with results of other studies, with adjusted R2 ranging from 30% to 50%. A validation test of the models, using independent permanent sample plots data, showed that the short-term predictions of the models for both pure and mixedwood stands are fairly unbiased. The models also gave reasonable average height growth and diameter growth trajectories for pure stands of the three species and also projected long-term mixedwood (aspen – white spruce mixture) volume growth dynamics reasonably well. The models also projected reasonably well (i) the effect of increasing initial stem density on average diameter and height, and (ii) the stand volume compared with an older version the Mixedwood Growth Model (ver. 2000A). It was concluded that explicitly linking tree height and diameter increment models does not only have a solid ecological basis, but it also results in a compatible prediction of tree growth and stand dynamics.

Comparing an individual tree growth model for Pinus halepensis Mill. in the Spanish region of Murcia with yield tables gained from the same area

To support forest management decisions on converting stands from even-aged to uneven-aged management, tree models are needed that can simulate both options. Therefore, an individual tree model for Pinus halepensis Mill. is compared with the respective yield table. The individual tree model is built from data of two Spanish forest inventories in this province and evaluated with published yield tables, which have been built from permanent observational plots. The individual tree model consists of a basal area increment model and a height increment model, both based on two measurements of about 4,000 trees from single species stands of Aleppo pine. The R² values of 0.362 and 0.107 for the basal area increment model and the height increment model, respectively, are within the range of other published models of this type. Comparing the model with the yield tables for different site indices, we find that our model matches the yield table well. Only in higher ages where the database for the yield table was poor, our model indicates higher basal area growth rates than the yield table.

Influence of canopy structure on the survival and growth of underplanted seedlings

This study explores the indirect relationship between forest structural measures and initial seedling survival and growth along a structural gradient between 64% to 92% canopy closure. The gradient was created by applying various levels of midstory removal to fifty 0.05 ha areas located within a mixed-hardwood riparian forest corridor. Twelve yellow-poplar (Liriodendron tulipifera L.) and cherrybark oak (Quercus pagoda Raf.) containerized seedling pairs were underplanted within each area. Canopy closure was estimated using hemispherical photography; height-to-canopy and basal area were recorded at each seedling pair. Survival, basal diameter, and height were monitored through two growing seasons. Species-specific mortality and height growth models were developed for one and two growing seasons following underplanting. The interaction of height-to-canopy and basal area along with canopy closure were found to be the most strongly related to mortality. Height to the forest canopy and initial seedling size explained the most variance in height increment. Although the height increment models possess limited predictive power (R2 range from 0.22 to 0.36), both mortality and growth analyses emphasize the importance of quantifying vertical canopy structure, along with the more commonly considered horizontal measures of forest structure (basal area and stem density), when evaluating seedling development beneath a forest canopy.

Individual tree height increment model for managed even-aged stands of ponderosa pine throughout the western United States using linear mixed effects models

A height increment model is developed and evaluated for individual trees of ponderosa pine throughout the species range in western United States. The data set used in this study came from long-term permanent research plots in even-aged, pure stands both planted and of natural origin. The data base consists of six levels-of-growing stock studies supplemented by initial spacing and other permanent-plot thinning studies for a total of 310 plots, 34,263 trees and 122,082 observations. Regression analysis is the most commonly used statistical method in forest modeling. However, research studies with repeated measurements are common in forestry and other biological disciplines. We choose the mixed models instead of the regression analysis approach because it allows for proper treatment of error terms in a repeated measures analysis. The model is well behaved and possessed desirable statistical properties. Our goal is to present a single height increment model applicable throughout the geographic range of ponderosa pine in the United States and by using only data from long-term permanent plots on sites capable of the productivity estimated by Meyer [Meyer, W.H., 1938. Yield of Even-aged Stands of Ponderosa Pine. US Department of Agriculture Technical Bull. 630].

Modelling the effect of temperature on height increment of Scots pine at high latitudes

The effect of temperature and precipitation on the height increment of Pinus sylvestris (L.) was modelled using data gathered from a total of 49 felled sample trees from five stands of Scots pine located along a latitudinal transect from the Arctic Circle up to the northern timberline in Finland. A multilevel mixed effects model and cross-correlation analysis of prewhitened time series was used to analyse the dependence between height increment and monthly meteorological observations. The effect of the mean July temperature of the previous year on height increment proved to be very strong at high latitudes (r > 0.7). The mean November temperature of the year before the previous affected statistically significantly on height increment in the three northernmost stands. There was no correlation between height increment and precipitation in any of the sites. The final height increment model based on all stands included tree age, long-term mean temperature sum of site, and the mean July temperature of the previous year as independent variables. According to the model, one degree’s change in July temperature results on average in 1.8 cm change in the next year’s height increment. There was a modest but significant polynomial age-effect. The proportion of explained variance (at the year level) was 74%. The July temperature dependence on height increment was shown to be very strong, suggesting a high value of height increment in climate modelling at the tree line.

An individual tree height increment model for mixed white spruce–aspen stands in Alberta, Canada

Individual tree-height increment models were developed for white spruce ( Picea glauca (Moench) Voss) and aspen ( Populus tremuloides Michx.) growing in the boreal mixed-species in Alberta. The models were formulated based on a selected base function (the Box–Lucas function), and the method of parameter prediction. Height increment was modeled as a nonlinear function of tree height, tree diameter, diameter increment, stand density, relative competitiveness of the tree in the stand, site productivity, and species composition. Since the data from permanent sample plots used in this study were time-dependent and cross-sectional, diagnostic techniques were applied to identify the models' error structure. Appropriate fits based on the identified error structure were accomplished using the nonlinear least squares procedures with a first-order autoregressive process. The models were also validated on independent testing data sets representing the population on which the models are to be used. Results showed that the average prediction biases were not significantly different from zero at α = 0.05, suggesting that the fitted models appropriately described the data and performed well when predictions were made. Biological implications of the variables that affect height increment in mixed-species stands were discussed.

Using Simultaneous Regression Techniques with Individual-Tree Growth Models

Abstract Individual-tree growth models basically consist of a number of equations (e.g., diameter or basal area increment model, height increment model, crown ratio model) to update tree parameters over time. These equations commonly are assumed to be independent, with parameters of each equation estimated separately rather than simultaneously with linear or nonlinear regression. However, the opposite assumption of interdependence seems more reasonable. A tree is a highly organized system, and assimilation of tissues in the form of diameter increment, height increment, and crown size does not occur independently. Procedures to simultaneously estimate systems of two or more interrelated models are well developed in the econometrics literature and are suggested as a viable alternative. Using more than 7,500 Norway spruce (Picea abies L. Karst) trees from the Austrian National Forest Inventory with remeasured breast height diameters and tree heights (5 yr interval), we compare an individual tree basal area increment model, a height increment model, and a crown ratio model separately using ordinary least squares (OLS) and simultaneously by applying two-and three-stage least squares (2SLS, 3SLS). Results indicate the presence of strong cross-equation correlations, especially between the basal area increment and height increment models. Thus, the 3SLS estimates are more efficient while the separately determined OLS estimates are biased. Two parameters that OLS indicates are significant are found to be nonsignificant when simultaneously estimating all system parameters with 3SLS. Such system simplification reduced the size of the variance-covariance matrix by 100 elements. For. Sci. 44(1):87-95.

Biased predictions for tree height increment models developed from smoothed ‘data’

Only two basic methods exist for obtaining tree height (H) increment data: felled tree measurements and remeasured height or height increment on standing forest trees. Because the former method is expensive (but reliable), and the latter has a large measurement error relative to the actual height increment, it is difficult to obtain good height increment data. The contradictory occurrence of high coefficients of determination for height increment models that are not based on felled-tree samples can only be explained by so-called height increment ‘data’ that is actually predicted from some heuristic function, usually of diameter. Such smoothed ‘data’ are not observable, not measurable, and have much variation removed. Use of smoothed data reduces the apparent problem of height increment modeling to a simplistic problem of using one function to estimate the smoothed predictions from another function. We illustrate this phenomenon with a controlled experiment. Using more than 7500 Norway spruce trees from the Austrian National Forest Inventory with remeasured heights (5 year interval), we built height increment models: (1) based on the difference in observed heights; (2) based on the difference in predicted heights using a heuristic function of diameter. Using the same model and input variables, the coefficient of determination was 3 times higher (0.44 vs. 0.14) using the smoothed increment ‘data’ than with the observed increment data. Furthermore the increment predictions based on the data sets with smoothed increment ‘data’ exhibited a significant overestimation. This demonstrates three things. First, that fit statistics measuring deviations about smoothed height increment data are misleading and strongly biased upward. Second, that the resulting models produce biased predictions that overestimate increment, especially for trees in an intermediate to suppressed social position in the stand. Third, that measurement errors in remeasured heights on standing trees are so large that the underlying height increment signal is nearly hidden ( R 2 = 0.14).

Modeling density-related Iodgepole pine height growth, using Czarnowski's stand dynamics theory

This paper presents a new density-dependent height-growth model for lodgepole pine (Pinuscontorta var. latifolia Engelm.) in Alberta. It predicts stand top height growth as a function of present top height, breast height age, and density. The model is an extension of Czarnowski's stand dynamics theory, using an iterative height increment model with variable site and density components. Using 946 annual growth periods from permanent sample plots, the calibration shows a good fit and simulates reasonable values, even beyond the database.