Height-Diameter Models for Three Subtropical Forest Types in Southern Brazil

Abstract

Total tree height (h) is often difficult to measure in natural forests. Regression models based on easily accessed variables like DBH (d) can be an alternative, since their assumptions are validated. The aims of this study are to: (i) calibrate specific and generic h-d models for three forest types (Seasonal Deciduous Forest, DEC; Mixed Ombrophilous Forest, MIX; and Dense Rainforest, DEN) in Santa Catarina state testing the regression assumptions and evaluating model quality; (ii) verify different h-d relationship between forest types. The dataset (1,766 measured tree h and 3,150 estimated h) was collected by Santa Catarina Forest and Floristic Inventory (IFFSC) in 418 systematically located sample plots. Models were calibrated for two datasets, one containing hypsometer measurements, the other h estimations made by field crews. Specific models were calibrated for species with at least 30 sampled trees. Residual normality, randomness and heteroskedasticity were evaluated by analytical methods. Confidence bands were generated by the Working-Hotelling method; z test for means was applied to compare models based on the two databases. The statistical parameters such as corrected Akaike Information Criterion provided evidences that logarithmic models were better adjusted to the data. Both datasets were statistically different for DEN and MIX. Differences in h-d relationships were found between forest types. The use of calibrated h-d models is an alternative for studying the relationships between these variables and to assess vertical structure patterns of forest communities, when h measurements are not feasible, although, for situations that more accurate h values are needed, they will not always provide reliable predictions.index terms: Tree height prediction; h-d relationship; forest inventory; regression assumptions; model calibration. resumoEm florestas naturais, a altura total das árvores (h) é, muitas vezes, difícil de medir. Nesses casos, modelos de regressão baseados em variáveis de fácil medição, como o DAP (d), são uma alternativa, desde que seus pressupostos sejam atendidos. Neste estudo, objetivou-se i) o ajuste de modelos hipsométricos para três tipologias florestais de Santa Catarina (Floresta Estacional Decidual, Floresta Ombrófila Mista, Floresta Ombrófila Densa), testando os pressupostos e avaliando a qualidade dos ajustes; ii) verificação de diferenças das relações hipsométricas entre as tipologias florestais e entre os modelos ajustados baseados em alturas medidas e estimadas. Os dados de 1.766 alturas medidas e 3.150 alturas estimadas em campo foram coletados pelo Inventário Florístico Florestal de Santa Catarina (IFFSC), em 418 unidades amostrais. Os modelos foram ajustados para ambos os conjuntos de dados. Modelos específicos foram ajustados para espécies com ≥ 30 árvores medidas; normalidade, aleatoriedade e homoscedasticidade dos resíduos foram avaliadas analiticamente. Bandas com intervalos de confiança foram construídas pelo método Working-Hotelling; teste z para médias foi aplicad...

Allometric height-diameter equations for Pinus pseudostrobus Lindl

“…This study's applicability is restricted to the local level (Diéguez-Aranda et al 2009) despite the high pressure of such equations demonstrated by Trincado and Leal (2006), a situation by which the tting of generalized height-diameter models, either traditionally or under the mixed-eects approach, is an alternative that extends the functionality of the information generated, reduces biases and better covers regional variability (Corral-Rivas et al 2014, Kulie²is et al 2014). Other similar works mention the goodness of t of such results in the collection of eld information and in the accuracy of the total height estimates to calculate the volume individually or by stand (Diéguez-Aranda et al , Vibrans et al 2015.…”

“…We analyzed ten allometric models (Table 1) chosen for having shown good estimates in other works (Huang et al 1992, Pece et al 2006, Trincado and Leal 2006, Juárez et al 2007and Vibrans et al 2015, in which k = height of 1.3 m where dbh is taken; b's = Parameters to be estimated. In choosing the equations, we considered the recommendations made by Fang and Bailey (1998) who suggest using only two-and threeparameter models, because expressions with four or more can lead to problems of convergence or instability of the estimates.…”

“…To obtain a better convergence of the parameters, we The goodness of t of the models was determined by the lowest values of the sum of the mean squared errors of prediction (SSE) and the root mean squared error (RMSE) Leal 2006, Vibrans et al 2015) and the highest values of the adjusted coecient of determination (R 2adj ), as well as the signicance of the parameters and the low values in their standard error (Diéguez-Aranda et al 2005). The homoscedasticity assumptions of the residuals were evaluated with the graphic analysis and the White (W) test, the autocorrelation of errors using the Durbin-Watson (DW) test (Barrios et al 2014) and the normality with the Shapiro-Wilk (SW) test (Vibrans et al 2015), considering the Kurtosis index (KI) (Martínez-López and Acosta-Ramos 2014). The accuracy of the estimates was evaluated with the absolute bias (B), the aggregate dierence in percentage (AD %) (Lencinas and Mohr-Bell 2007) and the graphical test of predicted data against observed data.…”

Estimación de la edad de Swietenia macrophylla (Meliaceae) a partir del diámetro normal en poblaciones del sureste mexicano

“…Para seleccionar la mejor ecuación, se realizó un análisis comparativo entre los valores resultantes del ajuste donde se tomó como referencia el menor valor de la raíz del cuadrado medio del error (RCME) y el mayor valor del coeficiente de determinación ajustado (R 2 ajus. ) (Pompa-García, De los Santos-Posadas, Zepeda-Bautista, & Corral-Rivas, 2011; Vibrans, Moser, Zimermann, & Mazaneuro, 2015). Posterior a ello, se verificó el cumplimiento de los supuestos de normalidad de los datos, homocedasticidad de los residuos y auto-correlación de los errores con las pruebas de Shapiro-Wilk…”

Amostragem da relação hipsométrica de Cerrado sensu stricto utilizando subparcelas

“…Nesse tocante, alguns trabalhos foram conduzidos em diferentes tipos de floresta nativa do Brasil, ou, povoamentos florestais inequiâneos, ou, multiâneos brasileiros, tais como, da Floresta Estacional Decidual do Rio Grande do Sul (Durlo e Denardi, 1998), Floresta Tropical Equatorial Ombrófila Densa do Maranhão (Batista et al, 2001), Mata Atlântica no Rio de Janeiro (Andrade et al, 2006), diferentes fisionomias de florestas em Minas Gerais (Costa et al, 2012), fragmentos de Floresta Ombrófila Mista no Paraná (Sanqueta et al, 2013), Floresta Aberta no Acre e Rondônia (Hess et al, 2014), Tipologias florestais em Santa Catarina (Vibrans et al, 2015) e Cerrado sensu stricto no Tocantins (Andrade et al, 2015;Santos et al, 2016). Santos et al (2016) avaliaram também, a amostragem da RH em mata nativa.…”