Additivity of tree biomass components using ratio estimate.

This study deals with the subject biomass estimation. The objective was to achieve the additivity of tree biomass components, which is defined as the compatibility among the component predictions and total tree biomass, using ratio estimates. The biomass estimation model was applied to black wattle trees in forest stands, which include a sample of 670 trees in an age range of 1 to 10.75 years. The adjusted model, in which the total biomass, or sum of predicted components, is a function of the stem volume multiplied by the Scalar Coefficients Proxy of Density, proved to be of great interest for biomass estimation and consistent when compared to the results obtained by WNSUR estimates (traditional method). The natural additivity of the tree biomass components was fully achieved, when modeling them by means of ratio estimation. Equations developed from the proportional behavior of the biomass components at different ages did not require the use of linear regression models and were obtained from calibration with the experimental data. The estimators resulting from these equations proved to be appropriate to make a generic model for correction of ratios coefficients at different ages.

Selection criteria for linear regression models to estimate individual tree biomasses in the Atlantic Rain Forest, Brazil.

BACKGROUND: Biomass models are useful for several purposes, especially for quantifying carbon stocks and dynamics in forests. Selecting appropriate equations from a fitted model is a process which can involves several criteria, some widely used and others used to a lesser extent. This study analyzes six selection criteria for models fitted to six sets of individual biomass collected from woody indigenous species of the Tropical Atlantic Rain Forest in Brazil. Six models were examined and the respective fitted equations evaluated by the residual sum of squares, adjusted coefficient of determination, absolute and relative estimates of the standard error of estimate, and Akaike and Schwartz (Bayesian) information criteria. The aim of this study was to analyze the numeric behavior of these model selection criteria and discuss the ease of interpretation of them. The importance of residual analysis in model selection is stressed. RESULTS: The adjusted coefficient of determination ([Formula: see text]) and the standard error of estimate in percentage (Syx%) are relative model selection criteria and are not affected by sample size and scale of the response variable. The sum of squared residuals (SSR), the absolute standard error of estimate (Syx), the Akaike information criterion and the Schwartz information criterion, in turn, depend on these quantities. The best fit model was always the same within a given data set regardless the model selection criteria considered (except for SSR in two cases), indicating they tend to converge to a common result. However, such criteria are not always closely related across different data sets. General model selection criteria are indicative of the average goodness of fit, but do not capture bias and outlier effects. Graphical residual analysis is a useful tool to this detection and must always be used in model selection. CONCLUSIONS: It is concluded that the criteria for model selection tend to lead to a common result, regardless their mathematical formulation and statistical significance. Relative measures of goodness of fitting are easier to interpret than the absolute ones. Careful graphical residual analysis must always be used to confirm the performance of the models.

Sampling system for estimating woody debris in an urban mixed tropical forest.

Woody debris, defined as standing and downed deadwood, consists in an essential component of the forest carbon stock. However, few studies have been carried out to get an efficient and accurate sampling procedure for estimating it. This work proposes two methodologies to estimate the woody debris volume in a Brazilian mixed tropical forest: 1) two-stage systematic sampling, using a mixed methodology, in which the Strand's method is applied to standing dead trees and stumps, and line intercept sampling is used to fallen trees and branches; and 2) ratio estimate of the sum of cross-sectional areas of deadwood pieces and forest basal area, aiming to obtain the total woody debris volume indirectly in the natural forest. Conversions for biomass and carbon stocks were made applying the mean basic density on the estimates of deadwood volumes. Both methodologies are accurate for woody debris volume estimates, with a sampling error equal to 16.1% (methodology 1) and 5.7% (methodology 2), at a 95% probability level. Thus, the methodology 2 has potential to be used in strategic forest inventories of woody debris, such as in National Forest Inventories, due to increasing importance of its quantification in all forest ecosystems.

Critical analyses when modeling tree biomass to ensure additivity of its components.

It is presented the theme additivity of biomass of tree components. To evaluate and discuss this context, experimental information collected in forests of Acacia mearnsii De Wild. was used. Equations for components (stem and crown) and total biomass were fitted by means of two procedures: 1) generalized nonlinear least squares and 2) weighted-nonlinear seemingly unrelated regressions. Analyzing the performance of the estimators, it can be concluded that the two tested procedures are equivalent. On the other hand, this conclusion differs when evaluated the consistency and efficiency of the estimators. Fitting equations for the components and for the total biomass by an independent way is not realistic, because from a biological point of view the estimates of biomass are inconsistent, i.e., are not additive. The biomass estimates of the components and of the total, resulting from equations adjusted by means of systems of equations, provided narrower confidence intervals in relation to the equations adjusted independently, and is therefore more efficient. The second procedure presents better biological properties and statistics to estimate allometric equations for biomass of the components and for the total when compared with the independent estimation, thus it should be the method to be used.

Ground level photosynthetically active radiation dynamics in stands of Acacia mearnsii De Wild.

The objective is to study the dynamics of photosynthetic radiation reaching the soil surface in stands of Acacia mearnsii De Wild and its influence on height growth in stands. This fact gives rise to the formulation of the following hypothesis for this study: "The reduction of the incidence of light inside the stand of black wattle will cause the inflection point in its height growth when this reaches 4 to 5 m in height, i.e. when the stand is between 2 and 3 years of age". The study was conducted in stands in the state of Rio Grande do Sul, Brazil, where diameters at breast height, total height and photosynthetically active radiation available at ground level were measured. The frequency tended to be more intense when the age of the stands increases. It was evident that a reduction of light incidence inside the forest occurred, caused by canopy closure. Consequently, closed canopy propitiated the competition of plants. This has affected the conditions for growth in diameter and height of this species, reason why it becomes possible to conceive the occurrence of an inflection point in the growth of these two variables, confirming the formulated hypothesis.

Comparison of data mining and allometric model in estimation of tree biomass.

BACKGROUND: The traditional method used to estimate tree biomass is allometry. In this method, models are tested and equations fitted by regression usually applying ordinary least squares, though other analogous methods are also used for this purpose. Due to the nature of tree biomass data, the assumptions of regression are not always accomplished, bringing uncertainties to the inferences. This article demonstrates that the Data Mining (DM) technique can be used as an alternative to traditional regression approach to estimate tree biomass in the Atlantic Forest, providing better results than allometry, and demonstrating simplicity, versatility and flexibility to apply to a wide range of conditions. RESULTS: Various DM approaches were examined regarding distance, number of neighbors and weighting, by using 180 trees coming from environmental restoration plantations in the Atlantic Forest biome. The best results were attained using the Chebishev distance, 1/d weighting and 5 neighbors. Increasing number of neighbors did not improve estimates. We also analyze the effect of the size of data set and number of variables in the results. The complete data set and the maximum number of predicting variables provided the best fitting. We compare DM to Schumacher-Hall model and the results showed a gain of up to 16.5% in reduction of the standard error of estimate. CONCLUSION: It was concluded that Data Mining can provide accurate estimates of tree biomass and can be successfully used for this purpose in environmental restoration plantations in the Atlantic Forest. This technique provides lower standard error of estimate than the Schumacher-Hall model and has the advantage of not requiring some statistical assumptions as do the regression models. Flexibility, versatility and simplicity are attributes of DM that corroborates its great potential for similar applications.

A model based on environmental factors for diameter distribution in black wattle in Brazil.

This article discusses the dynamics of a diameter distribution in stands of black wattle throughout its growth cycle using the Weibull probability density function. Moreover, the parameters of this distribution were related to environmental variables from meteorological data and surface soil horizon with the aim of finding a model for diameter distribution which their coefficients were related to the environmental variables. We found that the diameter distribution of the stand changes only slightly over time and that the estimators of the Weibull function are correlated with various environmental variables, with accumulated rainfall foremost among them. Thus, a model was obtained in which the estimators of the Weibull function are dependent on rainfall. Such a function can have important applications, such as in simulating growth potential in regions where historical growth data is lacking, as well as the behavior of the stand under different environmental conditions. The model can also be used to project growth in diameter, based on the rainfall affecting the forest over a certain time period.