Literature dealing with the development of height-age curves was reviewed. The advantages of “natural" height-age curves, which have variable rather than the "conventional" fixed form for all sites, were examined. Data collected from stem analyses of 53 dominant and 44 codominant Douglas-fir trees felled on five permanent sample plots in the University Research Forest, Haney, were analysed in order to develop natural height-age curves. A growth curve was constructed for each tree. Master curves were prepared for each plot and for each crown class. [The site index of each plot and for each crown class.] The site index of each plot was determined at the standard age of 100 years. Straight line regression equations of height over site index by age classes were developed. The feasibility of harmonization of the regression coefficients was examined. Sheaves of natural site-index curves were derived. The analysis was repeated three times with various modifications of the basic data. Analysis II was selected as the basis against which 11 sets of "site-index" curves derived by 10 different authors from data collected in various environments by various methods were compared. A comparison of three different height-age natural curves with the derived curves was made for very young trees. Also, the five-year growth in height on five permanent sample plots was compared with height-age curves derived from data collected on the same plots. The advantages of natural "site-index" curves as compared with standard height-age curves were discussed. / Forestry, Faculty of / Graduate

Tree and tree component weights of 63 forest-grown lodgepole pine trees were investigated. Data were collected from one tenth-acre plot located in south western Alberta. Both graphical and multiple regression techniques were used. Of the independent variables tested, tree basal area was most closely related to the component weights, with the exceptions of bole bark weight and total stem dry weight. The fresh and dry weights of bole bark were most closely associated with tree height, and total stem dry weight was most closely associated with dbh. Very reliable estimates of tree and tree component weights were obtained using regression techniques and the independent variables previously mentioned. The proportions of the component weights of the total tree weights were determined. The proportions were highly variable and widely dispersed about the mean. The tree characteristic most closely associated with the various proportions varied for the component being analysed. The proportion of the total tree weight contained in the stem, slash, bark and bole wood decreased with increasing tree size. The proportion represented by the needles, branches, merchantable stem, and crown increased with tree size. The crown and needle characteristics of lodgepole pine were investigated. Tree size, whether measured as stem weight in pounds or cubic foot stem volume (ob), was most closely correlated with dry needle weight (in pounds). The number of needles per cubic foot of stem volume increased with increasing tree size. The needle characteristics of lodgepole pine are highly variable. Needle length was significantly related to needle width. Needle length was not significantly related to any tree characteristics. The need to develop reliable sampling methods for biomass and fire control studies was discussed. Double sampling with regression appeared to offer accurate estimates with a minimum of weight measurement. The number of trees required to obtain a sample mean within plus or minus 10 per cent of the population mean at the 95 per cent confidence level is too large to be practical for most biomass and fire control studies. A higher standard error of estimate is probably more desirable, thus allowing a greater number of conditions to be sampled in order to increase the representativeness of the study. The mutual relationship between tree weight and tree volume was investigated. Tree volume was highly correlated with tree weight. Reliable estimates of tree weight were obtained from tree volume. Variation in moisture content and specific gravity, within and between trees was analyzed. These variables were surprisingly uniform and appear to pose only minor problems in weight scaling, for lodgepole pine. / Forestry, Faculty of / Graduate

Timber cruises in the interior of British Columbia are designed to meet precision requirements for estimating total net merchantable volume. The effect of this single objective design on the precision of other cruise-based estimates is not calculated. One key secondary objective, used in the stumpage appraisal of timber in the interior of the province, is estimation of the lumber recovery factor (LRF). The importance of the LRF in determining stumpage values and the fact that its precision is not presently calculated, prompted this study. Since the LRF is a complicated statistic obtained from a complex sampling design, standard methods of variance calculation cannot be applied. Therefore, the jackknife procedure, a replication technique for approximating variance, was used to determine the sampling error for LRF. In the four cruises examined, the sampling error for LRF ranged from 1.27 fbm/m³ to 15.42 fbm/m³. The variability in the LRF was related to the number of sample trees used in its estimation. The impact of variations in the LRF on the appraised stumpage rate was influenced by the lumber selling price, the profit and risk ratio and the chip value used in the appraisal calculations. In the cruises investigated, the change in the stumpage rate per unit change in the LRF ranged between $0.17/m³ and $0.21/m³. As a result, sampling error in LRF can have a significant impact on assessed stumpage rates. Non-sampling error is also a major error source associated with LRF, but until procedural changes occur, control of sampling error is the only available means of increasing the precision of the LRF estimate. Consequently, it is recommended that the cruise design objectives be modified to include a maximum allowable level of sampling error for the LRF. / Forestry, Faculty of / Graduate

Individual log scaling for the forest industry is a time consuming operation. Presented here are the design and prototype test results of an automated technique that will improve on the current speed of this operation, while still achieving the required accuracy. This is based on a technique that uses a television camera and graphics monitor to enable the operator to spot logs in images, which an attached processor can automatically scale. The system must be first calibrated however. Additional to the time savings are the advantages that the accuracy will be maintained, if not improved, and the operation may now be performed from a sheltered location. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The procedure used to sample crown timber before harvesting in B.C. is designed to estimate net volume per ha using systematically located angle-count plots where trees are selected with probability proportional to basal area. The primary purpose of the sample is to provide information for timber valuation and stumpage appraisal. Timber value is the most important population parameter for stumpage calculation, but it is not explicitly considered in the sampling design. The objective of this study was to modify the current sampling method to increase the efficiency for estimating value using model-dependent sampling theory. Eighteen model-dependent sampling strategies were developed from six subsampling methods using three estimators. The six subsampling methods were used to select trees from angle-count plots to estimate the relationship between cruiser-called and estimated tree value. Three subsampling methods used probability-based selection of trees and three methods used purposive-based selection of trees. Ratio, average ratio, and regression estimators were used with each method. The 18 strategies were tested using Monte Carlo simulation with 2000 samples at each of nine sample sizes in three test populations. The test populations were created by grouping angle-count plot data into mutually exclusive sets reflecting different stand characteristics. The sample sizes were n = 20,40, and 60 plots with m = n, 3n, and 5n subsampled trees. Individual tree value was estimated with regression equations that used variables closely related to the value of each species. The sampling strategies were evaluated for bias, sample variance, achieved subsample size, sampling cost, confidence interval coverage, and relative advantage against the current sampling method. The model-dependent subsampling methods using purposive selection of trees were more efficient than the current sampling method considering cost and variance. The purposive-based methods were biased up to about 5%; the probability-based methods were slightly less biased. The two most efficient methods were: i) purposive selection of trees with the highest estimated values in a plot; and ii) purposive selection of trees with estimated values within a given range to give a second-stage sample balanced on the auxiliary variable. The greatest efficiency was always achieved with one sample tree per plot. The current sampling method was unbiased for estimating value but required approximately twice as many plots to estimate value to the same level of precision as net volume. / Forestry, Faculty of / Graduate

Quantitative measures of stand density and stocking are very important because only with full knowledge of the growing stock can a forest be managed efficiently. Stocking is concerned with fraction of area occupied with trees. Density is related to the degree of crowding within the area occupied. These quantitative values are determined by parameters that could be measured on the ground and on aerial photographs. The methods used to estimate height, crown width, and crown closure from aerial photographs are thoroughly described. The writer also describes the stocking and density conditions under which trees grow, with illustrations by both theoretical models and actual sample plot crown models. Forty-seven sets of ground and photo-measurements were taken and analysed by simple and multiple regression methods. A comparison of photo and ground values was then made to evaluate the usefulness of aerial photographs for density and stocking measurements. The correlation of the ratio of height (Ht) to crown width (CW) from the ground and photo data to age, site index, crown closure, basal area, adjusted basal area, crowding factor and adjusted crowding factor were also studied. Eight assumptions regarding normality of density and full stocking were made so that the interrelationship between the individual density and stocking measurements could be studied more effectively. It is concluded that Ht/CW ratios are measurable from aerial photographs and shown that they are useful as a measure of stand density and stocking. / Forestry, Faculty of / Graduate

Weigh scaling is a method of estimating the total volume of timber harvested from a given region. The implementation of statistical sampling techniques in weigh scaling is described, along with related issues. A review of ratio estimators, along with variance estimators of the classical ratio estimator is conducted. The estimation of the variance of the estimated total volume is considered using jackknife- and bootstrap-based variance estimators. Weighted versions of the jackknife and bootstrap variance estimators are derived using influence functions and Fisher Information matrices. Empirical studies of analytic and resampling-based variance estimators are conducted, with particular emphasis on small sample properties and on robustness with respect to both the homoscedastic variance and zero-intercept population characteristics. With a squared error loss function, the resampling-based variance estimators are shown to perform very well at all sample sizes in finite populations with normally distributed errors. These estimators are found to have small negative biases for small sample sizes and to be robust with respect to heteroscedasticity. / Science, Faculty of / Statistics, Department of / Graduate

Volume and taper studies in Pinus patula and Cupressus lusitanica trees growing in Kenya forest plantations are discussed. The ultimate objective of the study was to find suitable models for estimating volumes and taper rates using two approaches for each parameter (i.e. volume and taper). These included producing volume models in the traditional way and by integrating taper models. Taper models derived from the best of the volume models were compared to the taper models produced from taper data in the traditional way to find out the efficiency of each approach. Data from the two species were used to fit a few popular volume and taper models. Trials were also made to develop new models. Of the popular volume models tested the logarithmic volume model was found to be giving very good estimates. Weighted models conditioned through the origin, by a technique proposed in the study, were also giving similar good estimates. Models weighted by current approach were, however, giving relatively poor estimates. Volume-based taper models were found to be giving biased diameter estimates along the tree profiles. However, when integrated for total volume, the volume estimates given seemed to be better than those given by the other taper models tested. Because of their bias in estimating the diameters and other points along the tree profile, volume-based taper models are not recommended for estimating volumes to any other points along the tree profiles. Other popular taper models were also giving biased diameter estimates. They lacked inflection points. When integrated for volumes, they were giving very poor estimates. Two fairly simple taper models have been proposed which have most of the characteristics needed in a taper model to give proper profile description. They have been recommended for constructing the inside volume tables and taper tables for the two species. They should also apply well in other conifers. One model describes profiles of trees with butt swell while the other describes trees with smooth stem forms. / Forestry, Faculty of / Graduate

Nine taper equations were tested to predict diameters inside bark along the stem for <i>Pinus oocarpa</i> Schiede trees growing in natural stands of central Honduras. A five parameter submodel predicted as well as an eight parameter model proposed by Kozak, 1988. Taper variation was explored between two geographic regions from which trees with different taper were suspected. Results showed that different site classes, not fully accounted for in the model, might have an effect on the prediction of taper in each region. Also, the effect of crown class and live crown ratio on prediction was evaluated. The model selected exhibited different prediction patterns for dominant and suppressed trees. On the other hand, live crown ratio did not appear to affect prediction. A computer program was written to use the taper equation developed to compute total and merchantable volume to different top diameter limits. / Master of Science

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