Leaf area distribution and alternative sampling designs for hybrid spruce tree crowns
Creators: name: Hailemariam, Temesgen
Publisher: name: University of British Columbia
Year: 2009

description: Three-dimensional populations such as tree crowns present unusual sampling problems owing to the variability of morphological attributes at different heights, relative horizontal positions, and cardinal directions of the crown. High within- and among-tree crown variation have also contributed to the difficulty of tree crown sampling and single tree leaf area (TLA - area available for photosynthesis) estimation. The two objectives of this research were to: 1) describe the distribution of leaf area in hybrid spruce (Picea engelmannii * glauca * sitchensis) crowns grown in the northwestern interior of British Columbia, and 2) to assess and evaluate sampling alternatives that consider variations in the radial and vertical distribution of foliage in estimating TLA of hybrid spruce crowns. To meet these objectives, data were collected and used to: 1) examine the spatial distribution of leaf area, 2) create independent test populations of trees, and 3) evaluate five sampling alternatives for obtaining TLA estimates. Three-dimensional graphs of leaf area per centimetre (APCM) at different heights and relative horizontal widths of tree crowns illustrated that APCM increases towards the top of the tree and the tip of first-order branches. Trees between 50 to 60 years of age showed the highest APCM, whereas trees older than 120 years showed the least APCM. To compare selected sampling designs, test populations were created using several non-linear equations and a bivariate Weibull distribution function. The precision of these models was substantially greater when 1) the seemingly unrelated regression (SUR) fitting method was used instead of the separate multiple linear regression (MLR) or composite fitting method, and 2) branch position from the tip of the tree relative to tree height (zi1) was used rather than relative to crown length (zi2). Also, bivariate Weibull an beta distribution functions resulted in more precise representations of APCM within tree crowns than the univariate Weibull and beta distribution functions. The bivariate distribution functions, unlike the univariate distribution functions, provided insights into positional (vertical and horizontal) variability of leaf area distribution in tree crowns. Five sampling designs were compared for mean square error, bias, sampling variance, distribution of the estimates, and cost. All sampling designs showed nearly zero bias, with the exception of the linear systematic sample selection procedure owing to the unequal inclusion probability of first-order branches and twigs. Stratified random sampling by tree height classes resulted in the lowest MSE values for the three sample sizes, followed by ellipsoidal, two-stage systematic, simple random, and two-stage unequal probability sampling. Two-stage unequal probability sampling consistently resulted in the least precise TLA estimates under different sampling intensities. Since the probabilities were based on branch and twig length, this reflects a poor relationship between twig leaf area and branch/twig length. [Scientific formulae used in this abstract could not be reproduced.]