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Breast height radial growth of 165 western red cedar (Thuja plicata Donn), 14.5 western hemlock (Tsuga heterophylla (Raf.) Sarg.) and 33 Douglas fir trees (Pseudotsuga menziesii (Mirb.) Franco), in young natural stands on the eastern side of the University of British Columbia Research Forest near Haney, B.C. was analysed. Individual tree parameters measured included breast height diameter, total height, age at breast height, radial growth over last five and ten years, crown width, live crown length, tree class, live crown ratio, height/age ratio, crown width/breast height diameter ratio, and height/ crown width. Stand parameters measured were number of trees per plot, average breast height diameter of plot, and basal area per acre of plot. Plots were of variable radius as determined in prism cruising. Growth was investigated from results of simple correlation coefficients and several multiple regression analyses computed on an IBM 7040. Causes of variation in growth were assessed by studying interaction of variables affecting growth patterns. Individual species have distinctly different modes of growth. Species react differently to changes in stand density. Radial growth can be determined from measurements of tree crowns; and crown development reflects changes in stand density. Difference between species are found as crown development varies with stand density changes. Crown dimensions of western hemlock are least sensitive to changes in stand density as measured by basal area per acre, crown width/breast height diameter, live crown ratio, or height/crown width. An understanding of how crown dimensions change with variation in stand density can be used to refine predictions of tree radial growth derived from crown measurements. / Forestry, Faculty of / Graduate

The nonindustrial private forest sector controls 58 percent of the nation’s commercial forest area. Timber output from the NIPF has been a major forest policy issue throughout this century. A long-run regional timber output projection model was developed for the NIPF sector. The model was based upon two key assumptions: (1) forest management intensity and timber output are inversely related to the forest landowner’s alternative rate of return, and (2) for the NIPF sector, the alternative rate of return is inversely related to the size of forest holding. The timber output model was based on a cross-classification of NIPF land by its physical characteristics (e.g., forest type) and economic characteristics (e.g., landowner’s alternative rate of return). The stratification objective was to create strata with a uniform timber output response to changes in the above characteristics. If the total forest resource is thought of in terms of a matrix, each characteristic serves as a stratification dimension, creating a matrix composed of “homogeneous timber output response cells.” The values of each cell can be used as observations in a regression analysis projecting NIPF timber output. For the NIPF, the size of forest holding would be a primary stratification dimension. Due to the relationships described above, stratification by size of forest holding constitutes stratification by the landowner’s alternative rate of return. Also, since the forest resource is physically uniform, the expected rate of return (marginal value growth percent) of the forest will be uniform within a cell. NIPF landowners base their timber output decision on the relationship between the expected and alternative rates of return, resulting in a convenient forest policy analysis tool. The model was applied to a study region, Virginia’s Coastal Plain, with satisfactory results. / Ph. D.

Measurements of DBH, upper diameters, merchantable height and total heights were made on 80 standing white oaks (<i>Quercus alba</i>) which were then felled for detailed measurements of the same parameters. The data obtained were used to evaluate the accuracy of standing tree measurements, to develop and compare volume equations that used upper diameter as one of the predictor variables and to examine the contributions of individual predictor variables to total volume prediction bias and precision. Relative bias ranged from 0.85% for DBH measurement errors to 2.88% for total height measurement errors. Relative standard deviation ranged from 1.52% to 10.13% for DBH and total height errors respectively. When both bias and precision ( standard deviation ) were considered jointly, the relative root mean squared error ranged from 1.75% to 10.48% for DBH and total height errors respectively. Upper diameter and merchantable height showed negative bias. A comparison of eight fitted models against the combined variable model revealed a gain in precision and a reduction in bias for models that used upper diameter as a third predictor variable. The improvement as based on the relative root mean squared error ranged from 28.8% to 71.3% for taped measurements. However, models that used upper diameter as a substitute for either DBH or merchantable height performed worse than the combined variable model. An analytic examination of the impact of measurement error on volume prediction bias showed that merchantable height errors accounted for most of the bias and that DBH and upper diameter errors contributed almost equal amounts(in absolute terms) to the volume bias. / Master of Science

A method was developed to approximate the diameter distribution of unthinned plantations of loblolly pine from whole stand predictions of stand attributes. The beta probability density function (pdf) and the Weibull pdf were used as models for the diameter distribution function for estimating a stand attribute (such as average diameter at breast height (dbh) or total volume per acre) and the whole stand estimation of the attribute was defined. The given estimates of k stand attributes from whole stand models, the k parameter of the pdf were estimated (recovered). Two types of parameter recovery models were constructed. The first used equations for the non-central moments of dbh. For the beta pdf, equations for the predicted first moment (average dbh) and second moment (basal area per acre/(0.005454 N)) were used to compute the analytic solution for parameter α and β. The endpoints of the pdf were defined to be the predicted minimum dbh minus 0. 6 inches and maximum dbh plus 0.6. In the case of the Weibull pdf, the parameter c was solved from the coefficient of variation which itself was computed from the predicted first and second non-central moments. Then given this value of c, b was solved for using the predicted average dbh. The parameter a was set equal to one-half predicted minimum dbh. The second type of parameter recovery model used volume as one of the stand attributes used to solve for the parameters. Due to failure of the numerical solution algorithms to consistently converge to a solution for the parameters, the beta pdf could not be used. For the Weibull though solutions were always possible. The parameters a and c were estimated as before and b was then solved using the diameter distribution yield equation for total volume per acre. The three models described above achieved a solution for the parameters 100% of the time. Comparison of the three using Kolmogorov-Smirnov statistics showed all three to be nearly equal in their ability to approximate the diameter distribution of stands. When compared to other conventional diameter distribution prediction methods (Burkhart and Strub 1974 and Smalley and Bailey 1974a), the parameter recovery models proved as good as or better than these other methods. In unthinned loblolly pine plantations the parameter recovery models proved to be a feasible alternative for predicting diameter distributions. The major advantage of the models is the numerical compatibility of the whole stand estimates of stand attributes and the diameter distribution estimates. Thus given whole stand estimates, such as basal area per acre or total cubic-foot volume per acre, the distribution of these attributes by diameter classes can be obtained. / Ph. D.

A diameter distribution prediction procedure for single species stands was developed based on the bivariate S_B distribution model. The approach not only accounted for and described the relationships between initial and future diameters and their distributions, but also assumed future diameter given initial diameter to be a random variable. While this method was the most theoretically correct, comparable procedures based on the definition of growth equations which assumed future diameter given initial diameter to be a constant, sometimes provided somewhat better results. Both approaches performed as well, and in some cases, better than the established methods of diameter distribution prediction such as parameter recovery, percentile prediction, and parameter prediction. The approaches based on the growth equations are intuitively and biologically appealing in that the future distribution is determined from an initial distribution and a specified initial-future diameter relationship. ln most appropriate. While this result simplified some procedures, it also implied that the initial and future diameter distributions differed only in location and scale, not in shape. This is a somewhat unrealistic assumption, however, due to the relatively short growth periods and the alterations in stand structure and growth due to the repeated thinnings, the data did not provide evidence against the linear growth equation assumption. The growth equation procedures not only required the initial and future diameter distributions to be of a particular form, but they also restricted the initial-future diameter relationship to be of a particular form. The individual tree model, which required no distributional assumptions or restrictions on the growth equation, proved to be the better approach to use in terms of predicting future stand tables as it performed better than all of the distribution-based approaches. For the bivariate distribution, the direct fit, parameter recovery, parameter prediction and percentile prediction diameter distribution prediction techniques, implied diameter relationships were defined. Evaluations revealed that these equations were both accurate and precise, indicating that the accurate specification of the initial distribution and the diameter diameter distribution. / Ph. D.

Mathematical methods of assessing the spatial autocorrelation associated with individual tree characteristics in forest stands were identified. These measures were used to investigate the spatial autocorrelation of discrete tree characteristics including the species, product, and defect classifications. With the exception of the species classification, none of the discrete tree characteristics examined showed any evidence of significant (α = 0.05) levels of spatial autocorrelation in loblolly pine stands. The significant autocorrelation of the species classification was probably due to past stand history or microsite variability rather than overall stand conditions such as age, density, or percent pine. The relationship between the level of spatial autocorrelation associated with basal area and several descriptive stand characteristics was also examined. No strong relationships were identified but trends were noticed between the autocorrelation measures and measures of stand competition such as basal area and crown competition factor. The measures of spatial association indicate positive autocorrelation between the characteristics of neighboring trees at very low levels of competition with the autocorrelation becoming increasingly negative as competition increases. At extremely high levels of competition, the spatial autocorrelation measures become positive again, reflecting the stagnated condition of the stand. Methods were developed, using the measures of spatial autocorrelation, to assign characteristics to individual trees in computer generated stands. These methods, applicable for discrete or continuous characteristics; assign the characteristics to individual trees depending on the spatial location of the individual tree and the locations and characteristics of its neighbors. / Ph. D.

Terrestrial laser scanning (TLS) may provide a way to increase timber value recovery by replacing manual timber cruising with a simple-to-use, cost-effective alternative. TLS has been studied in several trials worldwide. Past studies have not compared TLS based estimates with mill estimates of stem value and volume. Three differently stocked stands of hybrid poplar were selected for diameter, stem sinuosity and height measurement using manual cruising and TLS. Selected trees were harvested and transported to a mill where they were scanned and then processed into lumber and chips. Data gathered using both manual and TLS methods were used to obtain stem volume and value estimates to compare with mill estimates. Results indicated that TLS diameter measurements were more accurately matched to mill and manual measurements up to about 7.5 meters on the stem than above 7.5 meters on the stem in all three stands. Stem curvature comparisons indicated that the variation between TLS and mill centerline measurements was similar to the variation between repeat mill scan measurements of the same stems. Using TLS as a pre-harvest inventory tool showed that additional revenue could be obtained from the reallocation of saw-log and chip log volume to veneer logs of various sizes in all three stands. It was also shown that the sampling error required to estimate stand value was greater than was required to estimate stand volume within the same error limits. / Graduation date: 2012

Lidar is able to provide height and cover information which can be used to estimate selected forest attributes precisely. However, for users to evaluate whether the additional cost and complication associated with using Lidar merits adoption requires that the protocol to use lidar be thoroughly described and that a basis for selection of design parameters such as number of field plots and lidar pulse density be described. In our first analysis, we examine these issues by looking at the effects of pulse density and sample size on estimation when wall-to-wall lidar is used with a regression estimator. The effects were explored using resampling simulations. We examine both the effects on precision, and on the validity of inference. Pulse density had almost no effect on precision for the range examined, from 3 to .0625 pulses / m��. The effect of sample size on estimator precision was roughly in accordance with the behavior indicated by the variance estimator, except that for small samples the variance estimator had positive bias (the variance estimates were too small), compromising the validity of inference. In future analyses we plan to provide further context for wall-to-wall lidar-assisted estimation. While there is a lot of literature on modeling, there is limited information on how lidar-assisted approaches compare to existing methods, and what variables can or cannot be acquired, or may be acquired with reduced confidence. We expand our investigation of estimation in our second analysis by examining lidar obtained in a sampling mode in combination with Landsat. In this case we make inference about the feasibility of a lidar-assisted estimation strategy by contrasting its variance estimate with variance estimates from a variety of other sampling designs and estimators. Of key interest was how the precision of a two-stage estimator with lidar strips compared with a plot-only estimator from a simple random sampling design. We found that because the long and narrow lidar strips incorporate much of the landscape variability, if the number of lidar strips was increased from 7 to 15 strips, the precision of estimators with lidar can exceed that of estimators applied to plot-only SRS data for a much larger number of plots. Increasing the number of lidar strips is considered to be highly viable since the costs of field plots can be quite expensive in Alaska, often exceeding the cost of a lidar strip. A Landsat-assisted approach used for either an SRS or a two-stage sample was also found to perform well relative to estimators for plot-only SRS data. This proved beneficial when we combined lidar and Landsat-assisted regression estimators for two-stage designs using a composite estimator. The composite estimator yielded much better results than either estimator used alone. We did not assess the effects of changing the number of lidar strips in combination with using a composite estimator, but this is an important analysis we plan to perform in a future study. In our final analysis we leverage the synergy between lidar and Landsat to improve the explanatory power of auxiliary Landsat using a multilevel modeling strategy. We also incorporate a more sophisticated approach to processing Landsat which reflects temporal trends in individual pixels values. Our approach used lidar as an intermediary step to better match the spatial resolution of Landsat and increase the proportion of area overlapped between measurement units for the different sources of data. We developed two separate approaches for two different resolutions of data (30 m and 90 m) using multiple modeling alternatives including OLS and k nearest neighbors (KNN), and found that both resolution and the modeling approach affected estimates of residual variability, although there was no combination of model types which was a clear winner for all responses. The modeling strategies generally fared better for the 90 m approaches, and future analyses will examine a broader range of resolutions. Fortunately the approaches used are fairly flexible and there is nothing prohibiting a 1000 m implementation. In the future we also plan to look at using a more sophisticated Landsat time-series approach. The current approach essentially dampened the noise in the temporal trend for a pixel, but did not make use of information in the trend such as slope or indications of disturbance ��� which may provide additional explanatory power. In a future study we will also incorporate a multilevel modeling into estimation or mapping strategies and evaluate the contribution of the multilevel modeling strategy relative to alternate approaches. / Graduation date: 2013 / Access restricted to the OSU Community at author's request from June 21, 2012 - Dec. 21, 2012

A stand-level growth and yield model was developed to predict future diameter distributions of thinned stands of mixed Appalachian hardwoods. The model allows prediction by species groups and diameter classes. Stand attributes ( basal area per acre, trees per acre, minimum stand diameter, and arithmetic mean dbh) were projected through time for the whole stand and for individual species groups. Future diameter distributions were obtained using the three-parameter Weibull probability density function and parameter recovery method. The recovery method used employed the first two non-central moments of dbh (arithmetic mean dbh and quadratic mean dbh squared) to generate Weibull parameters. Future diameter distributions were generated for the whole stand and every species group but one; the diameter distribution of the remaining species group was obtained by subtraction from whole stand values. A system of tree volume equations which allow the user t o obtain total tree volume or merchantable volume to any top height or diameter completes the model. Volumes can be calculated by species group and summed to get whole stand volume. / M.S.