Modeling dominant height growth using permanent plot data for Pinus brutia stands in the Eastern Mediterranean region

Aim of the study: At current, forest management in the Eastern Mediterranean region is largely based on experience rather than on management plans. To support the development of such plans, this study develops and compares site index equations for pure even-aged Pinus brutia stands in Syria using base-age invariant techniques that realistically describe dominant height growth.Materials and methods: Data on top height and stand age were obtained in 2008 and 2016 from 80 permanent plots capturing the whole range of variation in site conditions, stand age and stand density. Both the Algebraic Difference Approach (ADA) and the Generalized Algebraic Difference Approach (GADA) were used to fit eight generalized algebraic difference equations in order to identify the one which describes the data best. For this, 61 permanent plots were used for model calibration and 19 plots for validation.Main results: According to both biological plausibility and model accuracy, the so-called Sloboda equation based on the GADA approach showed the best performance.Research highlights: The study provides a solid classification and comparison of Pinus brutia stands growing in the Eastern Mediterranean region and can thus be used to support sustainable forest management planning.Keywords: site index; Generalized Algebraic Difference Approach (GADA); Sloboda equation.

Dynamic top height models for several major forest tree species in Great Britain

In this paper, we present new dynamic top height models for 10 major species in Great Britain. These models for pure, even-aged stands replace the current, static top height-age curves published in the 1980s, which are no longer reliable in the light of the new data that have been added over the past decades. We followed the generalized algebraic difference approach (GADA) to build the new models and specifically focused on models derived from the Hessfeld IV and Chapman–Richards height-age base equations. We selected a multi-asymptote and polymorphic GADA version of the Chapman–Richards equation for all the species, with the anamorphic functional form as a special case derived from the non-significance of one of the global parameters. The new models are dynamic, accurate and robust, which will permit unbiased yield predictions from current top height-dependent yield simulators in Great Britain.

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.

Modelling individual tree diameter growth for Norway spruce in the Czech Republic using a generalized algebraic difference approach

Individual tree-based growth models precisely describe the growth of individual trees irrespective of stand complexity. These models are more useful than the stand-based growth models for effective management of forests. We developed an individual tree diameter growth model for Norway spruce (Picea abies /Linnaeus/ H. Karsten) using permanent research plot data collected from Krkonoše National Park in the Czech Republic. The model was tested against a part of the Czech National Forest Inventory (NFI) data that originated from the western region of the country. Among various models derived by a generalized algebraic difference approach (GADA), the GADA model derived from the Chapman-Richards function best suited to our data. Tree-specific parameters unique to each growth series, which describe tree-specific growth conditions, were estimated simultaneously with global parameters common to all growth series using the iterative nested regressions. The model described most of the variations in diameter growth for model calibration data (R²_adj = 0.9901, RMSE = 0.5962), leaving no significant trends in the residuals. A test against NFI data also confirms that the model is precise enough for predictions of diameter growth for ranges of site quality, tree size, age, and growth condition. The model also possesses biologically desirable properties because it produces the curves with growth rates and asymptotes that increase with increasing site quality. The GADA model is path-invariant and therefore applicable for both forward and backward predictions, meaning that the model can precisely predict diameter growth at any past ages of the trees.

Dynamic Site Index Equation for Thinned Stands of Even-Aged Natural Longleaf Pine

A dynamic site equation derived using the generalized algebraic difference approach was developed for thinned stands of natural longleaf pine (Pinus palustris Mill.) in the East Gulf region of the United States using 40 years of measurements on 285 permanent plots. The base model predicts height growth of trees once they reach 4.5 ft and was fit using a varying parameter for each tree and global parameters that are constant for all 3,267 trees. Parameters were estimated in one step using the dummy variable approach and a first-order autoregressive error term to account for serial correlation. The final base-age invariant equation allows the user to specify the number of years required for trees to reach 4.5 ft in height.

Dominant height growth equations including site attributes in the generalized algebraic difference approach

We present a new dynamic dominant height growth model based on Cieszewski’s generalized algebraic difference approach (GADA) advanced dynamic site equation strengthened by the use of explicit climate and soil variables (i.e., H = f(H0,T0, T, site conditions)). The results suggest that the inclusion of climatic variables would improve the applicability of the inter-regional model in regions in which climate and soil type lead to intra-regional variability. The new model reduces the bias present in a previous dynamic model that did not include climatic attributes and improves the model efficiency across the different age classes. Climate has a multiplicative effect on dominant tree growth in the early development stages (<20 years) and an additive effect in older stands.

Development of a basal area growth system for maritime pine in northwestern Spain using the generalized algebraic difference approach

A basal area growth system for single-species, even-aged maritime pine (Pinus pinaster Ait.) stands in Galicia (northwestern Spain) was developed from data of 212 plots measured between one and four times. Six dynamic equations were considered for analysis, and both numerical and graphical methods were used to compare alternative models. The double cross-validation approach was used to assess the predictive ability of the models. The data were best described by a dynamic equation derived from the Korf growth function using the generalized algebraic difference approach (GADA) by considering two parameters to be site specific. The equation was fitted in one stage using the base-age-invariant dummy variables method. In addition, the system incorporates a function for predicting initial stand basal area, in which the site-related variable was expressed as a power function of site index. This function can be used to establish the starting point for the projection equation when no inventory data are available. The two equations are compatible. The effect of thinning on basal area growth was examined; the results showed that there was no need to use a different equation to reliably predict postthinning basal area development. The nonlinear extra sum of squares method indicated differences in the model parameters for the two ecoregions (coastal and interior) defined for this species in the area of study.