Autoregressive moving average models of conifer crown profiles

Abstract

A time-series autoregressive moving average (ARMA) approach was used to develop stochastic models of tree crown profiles for five conifer species of the Sierran mixed conifer habitat type. Models consisted of three components: (1) a polynomial trend; (2) an ARMA model; and (3) random error. A Bayesian information criterion was used to evaluate alternative models. It was found that 70% of the crown profiles could be modeled using first-order ARMA [AR(l) or MA(l)] models, and that an additional 25% could be modeled using a white noise model [(AR(O)]. When the coefficients of the ARMA models were statistically significant, the models proved to be both visually and statistically an improvement over the polynomial trend (a Euclidean model). A binary classification system was used to determine if model type was related to tree or stand characteristics. Using this classification we found that it was possible to relate the appropriate model type to forest tree size and forest stand density with acceptable accuracy.

Modelling the Crown Profile of Western Hemlock (Tsuga heterophylla) with a Combination of Component and Aggregate Measures of Crown Size

“…Grace et al [41] found the azimuth angle of the largest branch on radiata pine (Pinus radiata D. Don) was variable but for two thirds of trees there was a preferred angle for the largest branch to be on the northern side of the tree in the southern hemisphere. Component approaches to crown profile modelling (e.g., [21,38]) and aggregated ones (e.g., [15][16][17]) have explicitly measured crown asymmetry. However, in both approaches the measures were combined to develop a model of average crown profile for each tree in order to be useful in process or structural functional models.…”

“…Aggregate measures describe the two-dimensional or three-dimensional outline of a crown without explicit recognition of the individual branches. Examples of aggregate measures include the vertical or overhead projection onto a horizontal plane (i.e., crown projection area), the horizontal "side-view" projected area acquired with specialised instruments such as the crown window [15] or through destructive sampling [16]; or contour maps made from high resolution digital images [17,18] or from terrestrial [19] or airborne laser scanning (e.g., [20]).…”

Conifer Crown Fuel Modeling: Current Limits and Potential for Improvement

“…Crown modeling efforts to date have focused almost exclusively on species-and size-dependent means. With the exception of the studies by Gill and Biging (2002) and Parsons et al (2011), there have been few efforts to quantify and integrate intrinsic variation into crown simulation models, as has been done in other forest modeling applications (e.g., Stage and Wykoff 1993).…”

“…Early work along these lines used paraboloid models to describe foliar and crown volumes (e.g., Mitchell 1975, Biging andWensel 1990). More recently, flexible nonparameteric (Doruska and Mays 1998) and stochastic (Gill and Biging 2002) crown profile modeling strategies have been advanced. One of the primary motivations for modeling crown geometry has been to better characterize tree competition via crown overlap metrics.…”

Conifer crown profile models from terrestrial laser scanning

“…Direct methods utilize regression analysis to calculate crown width as a function of other, more easily measurable tree attributes such as total tree height, crown ratio or crown length, relative height within the crown or largest crown width (Biging and Wensel 1990;Baldwin and Peterson 1997;Hann 1999;Marshall et al 2003;Crecente-Campo et al 2009). Gill and Biging (2002) modeled crown profiles from photographs for five conifer species. Limitations of their approach to delineating crown profiles included photographic distortion, shading of crown edge, and visibility of, at most, two crown profiles per tree.…”