A review of stand basal area growth models

Growth and yield modeling has a long history in forestry. The methods of measuring the growth of stand basal area have evolved from those developed in the U.S.A. and Germany during the last century. Stand basal area modeling has progressed rapidly since the first widely used model was published by the U.S. Forest Service. Over the years, a variety of models have been developed for predicting the growth and yield of uneven/even-aged stands using stand-level approaches. The modeling methodology has not only moved from an empirical approach to a more ecological process-based approach but also accommodated a variety of techniques such as： 1） simultaneous equation methods, 2） difference models, 3） artificial neural network techniques, 4） linear/nonlinear regression models, and 5） matrix models. Empirical models using statistical methods were developed to reproduce accurately and precisely field observations. In contrast, process models have a shorter history, developed originally as research and education tools with the aim of increasing the understanding of cause and effect relationships. Empirical and process models can be married into hybrid models in which the shortcomings of both component approaches can, to some extent, be overcome. Algebraic difference forms of stand basal area models which consist of stand age, stand density and site quality can fully describe stand growth dynamics. This paper reviews the current literature regarding stand basal area models, discusses the basic types of models and their merits and outlines recent progress in modeling growth and dynamics of stand basal area. Future trends involving algebraic difference forms, good fitting variables and model types into stand basal area modeling strategies are discussed.

Estimating tree and stand sapwood area in spatially heterogeneous southeastern Australian forests

Aims Natural and anthropogenic changes in forests can have important influences on transpiration and water production.Understanding the effects of increasing disturbances,due for example to climate change and forest harvesting,requires detailed information on how forest density and structural attributes relate to transpiration.Mean annual transpiration of eucalypt forest communities is often strongly correlated with total cross-sectional sapwood area.Our aim was to test an efficient method for estimating sapwood area at_(1.3)m height(SA_(1.3))in a large number of trees to understand the spatial heterogeneity of tree and stand sapwood area within and between forest communities,and develop allometric relationships that predict SA_(1.3)with forest inventory data.We also apply tree competition models to determine the degree to which the relationship between SA_(1.3)and tree basal area at_(1.3)m height(BABA_(1.3))is influenced by competition.Methods We visited 25 recently harvested southeastern Australian forest sites consisting of 1379 trees and 5 Eucalyptus species to evaluate a new efficient data collection method for estimating SA_(1.3)with tree taper and stump dimensions data using mixed effects models.The locations of 784 stumps within one 5-ha site were accurately mapped using an unmanned aerial vehicle(UAV),and four distance-dependent tree competition models were applied across the site to explain within-stand variation in the ratio of SA_(1.3)to BABA_(1.3).Data from 24 additional sites,consisting of ten 15 m radial plots per site,were used to analyse within-site variation in R_(Ha)(the ratio of stand sapwood area SA_(Ha)to stand basal area BABA_(Ha)).The radial plots were merged within each site to evaluate between-site variations in R_(Ha)across the landscape.For predicting SA_(Ha)with forest inventory data,we computed the relationship between SA_(Ha)and a new index of total stem perimeter per hectare,defined as√BA_(Ha)N_(T),where N_(T)is tree stocking density.Important Findings Our 1379 measured stems represent the most comprehensive measure of sapwood area,surpassing the 757 measured stems in native eucalypt forests published in literature.The species-specific R_(Ha) varied considerably across sites and therefore extrapolating SA_(Ha)with spatially distributed BABA_(Ha)maps and a generalized R_(Ha) would introduce local uncertainty.We found that the species-specific stem perimeter index was more effective at capturing variability in SA_(Ha)across the landscape using forest composition,structure and density data(R^(2):0.72–0.77).The strong correlation between tree SA_(1.3)and BABA_(1.3)improved slightly using tree competition models(R^(2)increased from 0.86 to 0.88).Relating SA_(Ha)to routinely measured forest inventory attributes within permanent plots and Light Detection and Ranging(LiDAR)data may provide opportunities to map forest water use in time and space across large areas disturbed by wildfire and logging.