Height-age Relationships Research Articles

Dynamic Top Height Growth Models for Eight Native Tree Species in a Cool-Temperate Region in Northeast China

In this study, we developed dynamic top height growth models for the eight important Chinese tree species Larix gmelinii var. principis-rupprechtii, Pinus tabuliformis Carr., Pinus sylvestris var. mongolica Litv., Picea asperata Mast., Quercus mongolica Fisch. ex Ledeb, Betula platyphylla Suk., Betula dahurica Pall. and Populus davidiana Dode based on age-height relationships. For this purpose, commonly growth data from long-term observations of permanent experimental plots are used, which ideally cover all development stages from stand establishment to final harvest. As such data were not available in the research area of Hebei Province in Northeast China, we used stem analysis data as well as tree height and annual shoot length measurements. The dataset consisted of 72 stands, 233 dominant trees and 10,195 observations of stem discs and annual shoot length measurements. Five dynamic base-age invariant top height growth models were derived from four base models with the generalized algebraic difference approach and fitted to our age-height data using nested regression techniques. According to biological plausibility and model accuracy the Chapman–Richards model showed the best performance for Picea asperata. This selected model accounted for 99% of the total variance in age-height relationship with average absolute bias of 0.2322 m, root mean square error of 0.3337 m and Radj2 of 0.9979, respectively. The distribution of the residuals was scattered around 0 and without visible trends, indicating that the fitness of the models was good. All developed models are able to generate top height growth curves representing the analyzed height growth data and can be utilized for predicting height growth on the base of current height and age of dominant trees. Additionally, they are the base for calculating the development of other relevant stand attributes such as basal area and volume growth. The determination of potential site productivity by the use of top height growth curves is a practical and convenient method for a simplified presentation of complex growth processes in stands and helps to create growth models, which facilitate implementing sustainable forest management practices in Mulan Forest.

SITE QUALITY ESTIMATIONS BASED ON THE GENERALIZED ALGEBRAIC DIFFERENCE APPROACH: A CASE STUDY IN ÇANKIRI FORESTS

ABSTRACT In this study, it is aimed that the dynamic site index models were developed for Crimean Pine stands in Sarikaya-Cankiri forests located in middle northern Turkey. The data for this study are 153 sample trees obtained from the Crimean Pine stands. In modeling relationships between height and age of dominant or co-dominant trees, some dynamic site index equations such as Chapman-Richards (M1, M2, M3), Lundqvist (M4 and M6), Hossfeld (M5), Weibull (M7) and Schumacher (M8) based on the Generalized Algebraic Difference Approach (GADA) were used. The estimations for these eight-dynamic site index model parameters with well as various statistical values were obtained using the nonlinear regression technique. Among these equations, the Chapman-Richards’s equation, M3, was determined to be the most successful model, with accounted for 89.03 % of the total variance in height-age relationships with MSE: 1.7633, RMSE: 1.3279, SSE: 1165.6, Bias: -0.0380. After determination of the best predictive model, ARMA (1, 1) autoregressive prediction technique was used to account autocorrelation problems for time-series height measurements. When ARMA autoregressive prediction technique was applied to the Chapman-Richards function for solving autocorrelation problem, these success statistics were improved as SSE: 868.7, MSE: 1.3183, RMSE: 1.1482, Bias: -0.06369, R2: 0.918. Also, Durbin-Watson statistics displayed that autocorrelation problem was solved by the use of ARMA autoregressive prediction technique; DW test value=1.99, DW<P=0.5622, DW>P=0.4378. The dynamic site index model that was developed has provided results compatible with the growth characteristics expected in the modeling of height-age relations, such as polymorphism, multiple asymptote, and base-age invariance.

Estimation of change in forest height growth

Abstract Forest height increment rate is related to the forest growth conditions. Data bases of previous forest inventories contain information about forest heightage relationship on large number of forest stands while repeated measurements of permanent sample plots provide an excellent reference for comparison. Repeated airborne laser scanning of forest stands is an additional source for the estimation of change in forest structure. In this study, height growth of middle-aged and older forest stands for about 10 year period was compared to an algebraic difference model on permanent sample plots (66) and for a sample of forest stands with repeated airborne laser scanning data (61). The model was based on a large dataset of forest inventory records from the period of 1984–1993. Statistically significant increased forest height growth was found in permanent sample plots based on tree height measurements (9 cm yr−1) as well in stands with repeated laser scanning data (4.5 cm yr−1) in South-East Estonia compared to the algebraic difference model. The difference between the two data sets was explained by their mean age and site class, but the increased forest height growth compared to the old forest inventory data indicates improved growth conditions of forests in the test area. The results hint also that empirical data-based forest growth models need to be updated to avoid biased growth estimates.

Dominant height growth and dynamic site index models for Crimean pine in the Kastamonu–Taşköprü region of Turkey

Some dynamic site index models based on the generalized algebraic difference approach (GADA) were fitted for Crimean pine (Pinus nigra J.F. Arnold subsp. pallasiana (Lamb.) Holmboe) stands in Taşköprü, Turkey. Data were obtained from 132 dominant trees representing the wide range of site quality in the region. Nonlinear regression analysis and a second-order continuous-time autoregressive error structure were applied. After autoregressive modeling, the fitted models were evaluated both statistically and graphically. The best results were obtained with the dynamic site index model derived from the Bertalanffy–Richards base equation, accounting for about the 99% of the total variance in height–age relationships in dominant trees, with an Akaike information criterion (AIC) value of 119.55 and root mean square error (RMSE) of 0.5446. The selected base-age invariant dynamic site index curves provided the polymorphism with multiple asymptotes and other realistic height growth patterns.

Chronology of fluvial terrace sequences for large Atlantic rivers in the Iberian Peninsula (Upper Tagus and Duero drainage basins, Central Spain)

This work analyses the chronology of fluvial terrace sequences of the two most important fluvial basins from central Spain draining to the Atlantic Ocean (Upper Tagus and Duero drainage basins). Both basins evolved under similar Mediterranean climatic conditions throughout the Pleistocene and present comparable number of fluvial terraces (16–17) after excluding the higher terrace levels of the Tagus (T1–T5) entrenched in the Raña surface. These higher “rañizo terraces” was formed in response to fan-head trenching in this high alluvial piedmont (+220 m) and therefore not properly controlled by Quaternary fluvial downcutting. The study accomplishes the implementation of multiple regression analyses for terrace height-age relationships. To transform relative terrace heights above the present river thalwegs (i.e. +100 m) in numerical ages a “height-age transference function” has been developed on the basis of preliminary statistical geochronological approaches proposed for Central Spain. The resultant height-age transference function gather 73 published geochronological data for terrace sequences, featuring a 3rd Order Polynomial Function (R2 0.90). This function describes the overall trend of valley downcutting for the last c. 2.3 Ma in Central Spain and is used to assign numerical ages to terrace levels at different relative elevation.

A comparison of alternative data sources for modeling site index in loblolly pine plantations

Site index curves are generally developed from one of three data sources: (i) permanent sample plots, (ii) temporary sample plots, or (iii) stem analysis data. Permanent sample plots are considered to be the best data source for modeling height–age relationships; however, due to time and cost constraints, analysts may consider using temporary sample plots or stem analysis data for equation fitting. Temporary sample plot and stem analysis data, although more quickly obtained, require assumptions that are often not met when modeling site index. The question becomes how models developed from temporary sample plot or stem analysis data compare with models developed from permanent sample plot data. Data from a region-wide study in loblolly pine (Pinus taeda L.) plantations were used to develop site index curves from each of the three data sources. A form of the Chapman–Richards model was used for all three data sources to guard against confounding and to discern differences among the data sources when modeling height–age relationships. For the comparison and evaluation of behavior of different functions, the Schumacher model was also fitted to the three data sources. Curves developed from temporary sample plot and stem analysis data did not reproduce the height growth pattern exhibited in permanent sample plots, although curves derived from temporary plots were closer to the height growth pattern.

Bayesian calibration and Bayesian model comparison of a stand level dynamic growth model for Sitka spruce and Scots pine

Growthmodelscontinuetobeofimportanceinmodernmulti-functionalforestrytoprovideforecasts.Bayesian calibrationsallowbothmodelstructureandparameterstobeassessedsimultaneouslyinaprobabilisticframework, providing a model with which forecasts and their uncertainty can be better understood and quantified using posterior probability distributions. A Bayesian calibration of a stand-level dynamic growth (SLeDG) model is carried out for both Sitka spruce and Scots pine in the UK for the first time. The calibration used the differential evolution Markov-Chain method to reduce the required number of iterations for inference. Two different model structures were considered for estimating local stand productivity: one using the measured height–age relationship, and one using estimated site yield class. The height–age relationship was shown to be more probable for both species in a Bayesian model comparison (total model probability =0.64 and 0.58 for Sitka spruce and Scots pine, respectively), although metrics of model performance were similar for both model structures (R 2 ≥ 0.88 in all variables). A complete calibration (using all data) of the more probable model structure was then completed, and excellent model fit was observed (R 2 > 0.95 for all variables in both species). Example forecasts using the output from the calibration were demonstrated, and are compatible with existing yield tables for both species. This method could be applied to other species or other model structures in the future.

Geographical variation in age-height relationships for dominant trees in Japanese cedar (Cryptomeria japonica D. Don) forests in Japan

In this study, we analyzed Japanese National Forest Inventory data to investigate the geographical variation in the relationship between tree height and age for dominant trees, and the effects of climatic conditions on these relationships. Our analysis focused on Cryptomeria japonica forests in 13 regions of Japan. The age–height relationships were classified into two regional groups that were distinguished by their climatic conditions. Several categories of climatic variables (warmth, solar radiation, precipitation, and snow depth) were significantly correlated with the parameters of a model for the age–height relationships. Our results also suggest the existence of a latitudinal cline for the maximum tree height of C. japonica in Japan. In regions with cold temperatures, deep snow, low solar radiation, and low summer precipitation, C. japonica shows a late-maturity pattern for height increase, with slow initial growth and a large maximum size. In regions with the opposite climatic conditions, it shows an early-maturity pattern with fast initial growth and small maximum size.

Conifer reinvasion of montane meadows following experimental tree removal and prescribed burning

Tree invasion of mountain grasslands and meadows, pervasive throughout western North America, has become a management concern. Restoration of these systems requires tree removal and possibly prescribed burning; however, subsequent reinvasion by trees may compromise these efforts. In this study, we assess patterns of tree seedling establishment 8years after tree removal (with and without burning) from 1-ha experimental plots in conifer-invaded meadows in the Oregon Cascades. We quantify variation in the timing, spatial distribution, and density of establishment of species with differing seral roles; compare effects of burning; and explore relationships with distance to and characteristics of adjacent, residual forests. Seedlings established continuously after tree removal, dominated by late-seral Abies grandis (cumulative plot densities of 116–460/ha). Early-seral Pinus contorta and Pseudotsuga menziesii were much less abundant (0–25 and 1–52/ha, respectively). Frequency (percentage of 5×5m subplots) and density of seedlings did not differ between treatments (burned vs. unburned), nor did seedling growth rates (inferred from height-age relationships). Seedling spatial distributions and relationships with distance to adjacent forest varied both within and among plots. On average, however, seedlings were concentrated along edges. In the 5-m outer band of subplots, frequency averaged 37% and density, 682/ha, compared to 18% and 140/ha in the remaining cores of the plots. Density of Abies was significantly greater along more shaded southern edges (north-facing) than along more exposed northern edges (south-facing), but it declined steeply with distance from edge, especially for southern edges. Plot-level density of Abies seedlings was also correlated with basal area of Abies in the adjacent forest (but not with tree density or summed height). Strong relationships of seedlings with distance, exposure, and characteristics of adjacent forests suggest that conifer reinvasion can be minimized by targeting tree removal to maximize distances to residual trees. However, absence of a treatment effect suggests that burning—critical for reducing woody residues—does not increase the probability of seedling establishment, particularly in systems in which late-seral species are the principal colonists.

Dynamic base-age invariant site index models for Tectona grandis in peninsular India

Data from 27 remeasured sample plots were used to evaluate dynamic base-age invariant site index models for teak (Tectona grandis) forests in Karnataka, India. The data were obtained in observational field studies covering a wide range of sites in Karnataka and provided up to three interval measurements per plot. All the functions were fitted simultaneously using iterative seemingly unrelated regression and a base-age-invariant method. The model evaluation criteria were bias, root mean square error and the adjusted coefficient of determination. The best results were obtained with the generalised algebraic difference equations derived from the Korf base model. The selected model accounted for 99.8% of the total variance in height–age relationships in dominant trees. The dynamic base-age invariant site index model proved to be effective and accurate in presenting polymorphic site index curves with multiple asymptotes. The new dynamic base-age invariant site index models based on generalised algebraic difference approach (GADA) methodology can be recommended for dominant height prediction and forest site quality evaluations in the teak forests in Karnataka, India.

Dynamic base-age invariant site index models based on generalized algebraic difference approach for mixed Scots pine (Pinus sylvestris L.) and Oriental beech (Fagus orientalis Lipsky) stands

Data from stem analysis of 397 dominant trees (198 Scots pine and 199 Oriental beech) were used to evaluate dynamic base-age invariant site index models derived from Bertalanffy-Richards, Hossfeld, and Lundqvist-Korf functions with the generalized algebraic difference approach (GADA) for mixed Scots pine (Pinus sylvestris L.) and Oriental beech (Fagus orientalis Lipsky) stands. These functions were compared with respect to residuals of these models; specifically, the evaluation criteria were bias (E), root mean square error (RMSE), absolute mean error (AME), adjusted coefficient of determination (R2adj), and Akaike information criterion. The best results were obtained with generalized algebraic difference equations derived from the base models of Bertalanffy-Richards for Oriental beech and Hossfeld for Scots pine. These selected models accounted for 95%-96% of the total variance in height-age relationships in dominant trees with bias of 0.049841 and 0.00171, RMSE of 1.55624 and 1.353736, AME of 0.940128 and 0.884034, and AIC of 723.55 and 1250.78 for Scots pine and Oriental beech, respectively. These dynamic base-age invariant site index models for the 2 tree species presented more effective and accurate polymorphic site index curves with multiple asymptotes than earlier site index models for Oriental beech and Scots pine. The important differences of height growth trend between developed base-age invariant site index models in this study and earlier site curves were determined by graphical comparisons for site index predictions. Therefore, the new dynamic base-age invariant site index models developed based on GADA methodology can be recommended for dominant height prediction and forest site quality evaluations in the mixed stands of these 2 species.

Factors Influencing Height-Age Relationships and Recruitment of Ponderosa Pine Regeneration in Northern Arizona

Factors Influencing Height-Age Relationships and Recruitment of Ponderosa Pine Regeneration in Northern Arizona

A National height-age model for Pinus radiata in New Zealand

BackgroundHistorically, a series of regional height-age functions have been used to predict height growth of Pinus radiata in New Zealand. However, for some regions there are no available models while other regions have more than one available model.MethodsTo remedy this situation, a new system of height-age growth models for P. radiata in New Zealand was developed from a nationwide database using nonlinear mixed modelling techniques.ResultsWhen tested by cross validation, a simple national model performed poorly compared to a series of models with different parameters for each region, demonstrating the existence of regional differences in the form of the height-age relationship. Examination of the regional behaviour suggested that the effect of temperature is best represented by a common-asymptote family of curves, while other factors such as water availability and nutrition appear to be better represented by anamorphic families of curves. A national height-age model reflecting this behaviour was developed. This model is a polymorphic form of the Bertalanffy-Richards function, with the slope parameter expressed as a linear function of latitude and elevation.ConclusionsThis general model was found to perform better than a series of regional models, and is therefore recommended as a general purpose height-age model for P. radiata in New Zealand.

Growth of a Pine Tree

The growth of a pine tree is examined by preparing “tree cookies” (cross-sectional disks) between whorls of branches. The use of Christmas trees allows the tree cookies to be obtained with inexpensive, commonly available tools. Students use the tree cookies to investigate the annual growth of the tree and how it corresponds to the number of whorls on the tree. Height–diameter and height–age relationships are also investigated. While aimed at high school classes, the procedure can be adapted for younger students.

WHITE SPRUCE MEETS BLACK SPRUCE: DISPERSAL, POSTFIRE ESTABLISHMENT, AND GROWTH IN A WARMING CLIMATE

Local distributions of black spruce (Picea mariana) and white spruce (Picea glauca) are largely determined by edaphic and topographic factors in the interior of Alaska, with black spruce dominant on moist permafrost sites and white spruce dominant on drier upland sites. Given the recent evidence for climate warming and permafrost degradation, the distribution of white spruce is expected to expand, but the transition from black to white spruce may be dispersal limited: unlike the semi‐serotinous black spruce, postfire regeneration of white spruce relies on seed dispersal from unburned areas. To determine the relative roles of dispersal, establishment, and growth in recruitment of white and black spruce, we studied postfire spruce regeneration in a 21‐year‐old burn across a white spruce–black spruce transition in the interior of Alaska. Although prefire spatial distributions of adults of the two species were well separated along the topographic sequence from upland to floodplain sites, the spatial distributions of recruits overlapped considerably. Even >700 m away from its seed source, white spruce sapling density on typical black spruce sites was high enough to form fully stocked stands. In contrast, black spruce regeneration was sparse on typical white spruce upland sites. Establishment rates of both species, estimated from a statistical model, were highest in mossy, wet depressions, which tended to have a thick residual postfire organic layer (∼10 cm). On all site types, height growth rates inferred from age–height relationships were comparable for recruits of both species. On typical black spruce sites ≥300 m into the burn, white spruce was younger (and, therefore, shorter) than black spruce due to the timing of masting events following the fire. There was no indication that dispersal, establishment, or edaphic constraints on juvenile growth limit white spruce's capacity to invade typical black spruce stands during the recruitment stage in our study area. It is unlikely that white spruce recruits would persist to the adult stage if the permafrost returned to the original prefire levels during future postfire succession. However, if permafrost continues to degrade under climate warming, transition to a white spruce‐dominated landscape could be rapid.

Adjustment of the age–height relationship for uneven-aged black spruce stands

Site index (SI) is commonly used in natural stands, even when their diameter distribution deviates from that of the monospecific, even-aged, fully stocked stands used to develop basic age–height relationships. Since deviations from basic age–height trajectories can be reflected in deviations of stand diameter distribution from a bell shape, we incorporated different diameter diversity indices into an age–height equation to help improve height predictions and determine which index is best related to stand dominant height. This procedure was performed using black spruce ( Picea mariana (Mill.) BSP) stands from a large network of permanent sample plots established across the province of Quebec, Canada. The age–height model that minimized the Akaike’s information criterion used the Shannon evenness index (ESh) as an equation modifier accounting for the diameter diversity variable. The model showed that for stands established on relatively poor sites (SI = 9), no substantial differences in dominant height were found between two contrasting ESh values. For SI = 15, however, the larger ESh value increased the dominant height by as much as 1 m at 80 years. These results suggest that introduction of ESh into an age–height model can improve calculation of site index, particularly in regions characterized by the presence of numerous uneven-aged stands.

New dynamic site equation that fits best the Schwappach data for Scots pine ( Pinus sylvestris L.) in Central Europe

Using historical growth series data of Scots pine ( Pinus sylvestris L.) in Central Europe we examine all the dynamic site equations previously used for modeling the height growth of this species as well as a new dynamic site equation that has not been used previously in the context of this forestry data. The tested models included two groups of anamorphic and polymorphic dynamic site equations (three-dimensional site–height–age models, such as Y = f( t, t 0, y 0)). One group of the models is based on the algebraic difference approach (ADA) implementation of different, preexisting base equations (two-dimensional equations, such as Y = f( t)). The other group of models is based on newer generalized algebraic difference approach (GADA) formulations of new site–height–age relationships that may use older models only as a part of their structure. The models were selected because they were relevant to Scots pine height growth modeling in other studies. We compared all the models with each other in terms of the sum of square deviations associated with fitting them simultaneously to all sites represented by the Scots pine data. All the fits were based on base-age invariant stochastic regressions, in which the global model parameters that are common to all growth series are estimated simultaneously with the site-specific effects that are different for each of the site productivity series. Cieszewski's model [Cieszewski, C.J., 2005. A new flexible GADA based dynamic site equation with polymorphism and variable asymptotes. PMRC Technical Report 2005-2] best described the data.

Boreal mixedwood tree growth on contrasting soils and disturbance types

Mixedwood forests are an ecologically and economically important ecosystem in the boreal forest of northern Canada. The objectives of this study were to (i) compare the age–height relationships for dominant tree species growing on two contrasting soil types and originating from different disturbances (logging versus wildfire), and (ii) determine the influence of competition on tree growth. Eight stands were selected that encompassed two age-classes replicated on two soil types (clay loam and sand) in a split-plot design. Four of the eight stands originated from logging (21–26 years old), and <F"Times">the four others originated from wildfires (80 years old). Nonlinear age–height analyses were used to compare annual height and radial increment growth of black spruce (Picea mariana (Mill.) BSP), jack pine (Pinus banksiana Lamb.), and trembling aspen (Populus tremuloides Michx.). Species, soil type, and size class explained significant amounts of the measured variation in the age–height models. Aspen, black spruce, and jack pine were 16%, 27%, and 19% taller, respectively, on clay soils than on sandy soils at the burned stand. Tree heights did not differ significantly among species or between soil types in logged stands. Diameter growth decreased as competition increased for black spruce and jack pine in the burned stands. The results for these three important boreal tree species are discussed in the context of sustainable forestry for boreal mixedwood forests.

Age structure of Picea schrenkiana forest along an altitudinal gradient in the central Tianshan Mountains, northwestern China

Size distribution and age structure of Schrenk spruce ( Picea schrenkiana Fisch. et Mey.) forest along the altitudinal gradient on the central Tianshan Mountains was studied in this paper. The forest was divided into three transects, i.e., lower limit (1500–1700 m), mid-altitude (1800–2400 m) and upper limit (2500–2700 m). Age of each individual was estimated by the age–height relationships of seedlings or saplings and the age–DBH (diameter at breast height) relationships of big trees. A reverse-J shape age structure was found in the mid-altitude transect; the age structure of the low altitude transect was characterised by the dominance of young trees, whereas the transect of high altitude lack of young seedlings and saplings. It is implied that different limiting factors play important roles in shaping the age structure and regeneration of forest at different altitudes. In the mid-altitudinal transect, density dependent competition between trees is probably the most important influencing factor. We propose that limiting environmental factors, e.g. temperature and precipitation, play important roles in determining the age structure of P. schrenkiana population in the high or low limit transacts.

Saguaro (Carnegiea gigantea, Cactaceae) age–height relationships and growth: the development of a general growth curve

Because the growth rate of saguaros varies across different environments, past studies on saguaro population structure required extensive data collection (often over many decades) followed by site-specific analysis to estimate age at the sampled locale. However, when height-growth data from different populations are compared, the overall shape of the growth curves is similar. In this study, a formula was developed to establish saguaro age-height relationships (using stepwise regression) that can be applied to any saguaro population and only requires a site-specific factor to adjust the curve to the local growth rate. This adjustment factor can be established more efficiently and requires less data than the full analyses required for previous studies. Saguaro National Park East (SNP-E) was used as the baseline factor, set to 1.0. Results yielded a factor of 0.743 for SNP West. When the formula was applied to 10-yr interval data from Organ Pipe Cactus National Monument (OPCNM) in Arizona, USA, this location had a factor of 0.617 (relative to SNP-E). With this formula and relatively little field sampling, the age of any individual saguaro (whether the individual was sampled or not) in any population can be estimated.