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Relationships between coastal Douglas-fir stand biomass and stand characteristics Wong, Ann Yone 2002

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RELATIONSHIPS BETWEEN COASTAL DOUGLAS-FIR STAND BIOMASS A N D STAND CHARACTERISTICS by A N N YONE WONG B.S.F., The University of British Columbia, 1999 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES THE FACULTY OF FORESTRY We accept this^ nWs as confopmin^ to the required standard THE UNIVERSITY OF BRITISH COLUMBIA .. September 2002 Ann Yone Wong, 2002 In p resen t ing this thesis in part ial fu l f i lment of t h e requ i rements f o r an advanced degree at t h e Univers i ty o f Brit ish C o l u m b i a , I agree that t h e Library shall make it f reely available f o r re ference and study. I fu r ther agree that permiss ion f o r extens ive c o p y i n g o f th is thesis f o r scholar ly pu rposes may b e gran ted by the head of my d e p a r t m e n t o r by his o r her representat ives. It is u n d e r s t o o d that c o p y i n g or pub l i ca t i on o f this thesis fo r f inancial gain shall n o t be a l l owed w i t h o u t my w r i t t e n permiss ion . D e p a r t m e n t o f f o < e s \ 8 , e > o ^ c e & W a ^ c ^ a x i ^ f c The Univers i ty of Brit ish C o l u m b i a Vancouver , Canada Date Se^t 3£>> Zx>e z_ DE-6 (2/88) ABSTRACT The purpose of the study was to investigate how the aboveground tree biomass components (stem, branches, and foliage) and the ratios between these biomass components change with age, site quality, initial spacing, and total stand volume. The species studied was coastal Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco). To examine stands of various stand characteristics, virtual stands were generated from the Tree and Stand Simulator (TASS), a provincial growth and yield model. The stands ranged in site index (height at 50 years breast-height age) from 20 to 40 m at 5 m site index intervals, initial plant spacing of 1.0 to 5.0 m at 0.5 m spacing intervals, and from 10 to 200 years at 10-year intervals, for a total combination of 900 stands. Published tree biomass equations from the Pacific Northwest were applied to these generated stands to produce a stand-level biomass estimate for each stand. Stand-level biomass regressions were also developed from the modelled stands. Over the modelled 200-year horizon, stand-level stem and branch biomass is expected to increase, whereas foliage biomass is predicted to increase then plateau or peak then decline. At a given age, predicted biomass was higher for denser stands and richer sites. However, for a given total stand volume and initial spacing, predicted biomass was slightly higher for poor sites. At a given volume, more dense stands also had lower predicted stem and branch biomass, and higher predicted foliage biomass. In terms of the proportion ratios among components of biomass, the proportion of foliage and branch biomass in total aboveground tree biomass over time was predicted to decrease then plateau, whereas the proportion of stem biomass was predicted to increase then plateau. For a given stand volume, denser stands had proportionally less predicted aboveground tree biomass in stem biomass and proportionally more in foliage and branch biomass. From the stand-level biomass regression analysis, it was found that in addition to total stand volume, other stand variables, especially basal area, improved the predictive abilities of the stand-level biomass equations. ii TABLE OF CONTENTS ABSTRACT ii LIST OF TABLES v LIST OF FIGURES vi ACKNOWLEDGEMENTS viii 1. INTRODUCTION 1 2. RELATIONSHIPS BETWEEN STAND BIOMASS AND SELECTED STAND CHARACTERISTICS 3 2.1 INTRODUCTION 3 2.2 BACKGROUND 3 2.2.1 Biomass and Volume 3 2.2.1 Stem Biomass 4 2.2.2 Branch Biomass 5 2.2.3 Foliage Biomass 6 2.2.4 Tree-level Biomass Equations 7 2.2.5 Tree to Stand-Level Biomass 17 2.3 METHODS 18 2.3.1 Criteria for Selecting Equations for Further Analysis 19 2.3.2 Stand Data Description 19 2.3.3 Tree to Stand-Level Biomass 21 2.3.4 Initial Spacing and Stand Density 21 2.4 RESULTS and DISCUSSION 22 2.4.1 Selection of Equations for Further Analyses 22 2.4.2 Range of Component Biomass Values 24 2.4.3 Biomass versus Volume 29 2.4.4 Biomass versus Age, Site Quality and Initial Spacing 30 2.4.4.1 Predicted biomass components 30 2.4.4.2 Predicted stem biomass 32 2.4.4.3 Predicted branch biomass 34 2.4.4.4 Predicted foliage biomass 35 2.4.5 Biomass/ Volume Ratios versus Age, Site Quality and Initial Spacing 39 2.4.5.1 Stem Biomass/ Volume Ratios : '. 39 2.4.5.2 Branch Biomass/ Volume Ratios 40 2.4.5.3 Foliage Biomass/ Volume Ratios 41 2.4.6 Component Biomass Ratios versus Age, Site Quality and Initial Spacing 43 2.4.6.1 Ratios of stem biomass to total biomass 44 2.4.6.2 Ratios of foliage and branch biomass to total biomass 46 2.4.7 Component Biomass Ratios versus Volume 48 2.5 SUMMARY 50 3. PREDICTING STAND BIOMASS USING REGRESSION ANALYSES 51 3.1 INTRODUCTION 51 3.2 BACKGROUND 57 3.3 METHODS 53 3.4 RESULTS and DISCUSSION 56 3.4.1 Biomass and Volume 56 3.4.2 Biomass Using Volume and Selected Stand Characteristics as Predictors 61 3.4.2.1 Regressions based on inventory variables 61 3.4.2.2 Regressions based on all variables 65 3.4.3 Component Biomass Ratios and Selected Stand Characteristics 69 3.5 SUMMARY 74 4. CONCLUSIONS 75 5. RECOMMENDATIONS 80 LITERATURE CITED 81 APPENDIX 1: Summary of Additional Stand Statistics From TASS 90 APPENDIX 2: Summary of Tree-level Statistics in A l l Douglas-fir Stands 91 APPENDIX 3: Summary of Component Biomass Values (t/ha) From Reported Studies 92 APPENDIX 4: Ratio of Foliage Biomass to Stem Biomass Over Time 95 APPENDIX 5: Ratio of Branch Biomass to Stem Biomass Over Time 95 APPENDIX 6: Proportion of Foliage Biomass to Stem Biomass Over Total Volume 96 APPENDIX 7: Proportion of Branch Biomass to Stem Biomass Over Total Volume 96 iv LIST OF TABLES Table 1: Coastal Douglas-fir component biomass equations (dry weight) 9 Table 2: Summary of stand statistics from TASS 20 Table 3: Range of biomass estimates (t/ha) by various equations at stand age 30 25 Table 4: Range of biomass estimates (t/ha) by various equations at stand age 60 25 Table 5: Summary of predicted stand-level component biomass equations and model fit using stand volume (m3/ha) 57 Table 6: Correlation matrix between stem stand biomass (kg) and stand characteristics 58 Table 7: Correlation matrix between branch stand biomass (kg) and stand characteristics 58 Table 8: Correlation matrix between foliage stand biomass (kg) and stand characteristics 59 Table 9: Summary of predicted stand-level component biomass equations and model fit using stand volume and inventory variables 63 Table 10: Summary of predicted stand-level component biomass equations and model fit using stand volume and all other variables available in TASS 67 v LIST OF FIGURES Figure 1: Possible foliar biomass trends over time 6 Figure 2: Foliage biomass (t/ha) predicted by equations in Table 1 for stands varying in site productivity, age and initial spacing at different stand mean diameters 24 Figure 3: Comparison between component biomass over time from this study and other studies.: 27 Figure 4: Comparison between component biomass over stand volume from this study and other studies 28 Figure 5: Relationship between stand-level component biomass and stand volume 30 Figure 6: Number of trees in 1 m and 5 m spaced stands of SI 20 and 40 over time 31 Figure 7: Stem biomass versus stand density 32 Figure 8: Stem biomass over time 33 Figure 9: Relationship between stem biomass and relative stand density 33 Figure 10: Branch biomass over time 34 Figure 11: Relationship between branch biomass and relative stand density 35 Figure 12: Relationship between foliage biomass and relative stand density 36 Figure 13: Foliage biomass over time 37 Figure 14: Stem biomass over total volume ' 40 Figure 15: Relationship between branch biomass and total stand volume 41 Figure 16: Relationship between foliage biomass and total stand volume 42 Figure 17: Foliage, branch and stem proportions to total biomass for all spacing and SI stands over time 44 Figure 18: Percentage of stem biomass to total biomass over time 45 Figure 19: Percentage of foliage biomass in total biomass over time 47 Figure 20: Percentage of branch biomass in total biomass over time 47 Figure 21: Percentage of stem biomass in total biomass over total volume 48 Figure 22: Percentage of foliage biomass in total biomass over total volume 49 Figure 23: Percentage of branch biomass in total biomass over total volume 49 Figure 24: Residual plot of stand foliage biomass from Equation 33, Table 5 60 Figure 25: Stem biomass versus total volume for A) volume-based Equation 29 and B)inventory-based Equation 37 65 vi Figure 26: Percentage of predicted branch biomass to predicted stem biomass using volume-based functions, inventory-based functions, and all variables-based functions plotted against observed proportion biomass ratios from Gholz et al. (1979) equations 71 Figure 27: Percentage of predicted branch biomass to predicted stem biomass using volume-based functions, inventory-based functions, and all variable-based functions plotted against observed proportion biomass ratios from Kurz (1989) equations 72 Figure 28: Percentage of predicted branch to predicted stem biomass over total volume for volume-based equations and all variables-based equations using Gholz etal. (1979) based equations 73 Figure 29: Percentage of predicted branch to predicted stem biomass over total volume for volume-based equations and all variables-based equations using Kurz (1989) based equations 73 vii ACKNOWLEDGEMENTS I thank my supervisor, Dr. Gary Bull, for his advice and encouragement. I also thank Dr. Werner Kurz for his valuable inputs and introducing me to biomass research. I owe special thanks to Dr. Valerie LeMay for teaching me biometrics and her time spent in helping me with the regression analyses. My other supervisory members, Warren Mabee and Temesgen Hailemariam, have also been very helpful. Funding support was provided by the B C Ministry of Forests. I would like to thank Ken Polsson, Dr. James Goudie, and Dr. Ken Mitchell in the BC Ministry of Forests, Research Branch, for their TASSaata and help. I am also grateful to Sharon Hope for her review and to Tim Shannon and Kelly Wong for their programming support. Special thanks goes to my lab and office buddies who have made graduate school an enjoyable experience. I also thank my sister for keeping me grounded. Lastly, I would like to thank my family and friends for their endless support, patience, and encouragement. viii 1. INTRODUCTION Although most foresters and scientists have traditionally focused on forest volume for timber production, there has been a growing interest in forest biomass largely due to an expanding recognition of the ecological and economic role of forests. Biomass is the total quantity or mass of organisms (i.e. trees) in a given area (i.e. forest) (The New Oxford Dictionary of English 1998). Traditionally, biomass is useful in: 1) calculating the weight of pulp and paper (Parde 1980), 2) measuring the biological productivity of forest ecosystems (Duvigneaud 1971, O'Neill and de Angelis 1981), 3) quantifying forest fuels for forest fire modelling (Kurucz 1969, Brown 1978), and 4) substituting energy-intensive sources particularly during times of oil shortages (Stout 1985, Canadian Forest Service 1998). Now there is renewed interest in biomass estimates given the concern over climate change impacts on humans, plants and animals. Because trees can sequester and store carbon from the atmosphere in their biomass, scientists are interested in quantifying the amount of carbon in biomass, biomass-carbon relations and the dynamics of biomass-carbon in a stand. Under the United Nations Framework Convention on Climate Change (UNFCCC), forests are recognized as a carbon pool (UNFCCC 1997). Furthermore, under the UNFCCC, a nation is to report on the carbon in aboveground biomass as part of their greenhouse gases inventory. The carbon in trees is often determined by using a biomass to carbon conversion factor and is approximately 0.5 (IPCC 1996). Therefore, it is important to determine the amount of biomass in a forest before examining the carbon in a forest. In this study, I will examine the ranges of biomass in pure, even-aged stands of coastal Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) over site productivity, initial plant spacing, age, and total stand volume. Stand-level biomass was studied rather than tree-level biomass 1 because stands are the basic unit of forest management and planning, and stand-level data are readily available in forest inventories. In this context, the four objectives of this study are: 1. To explore the relationships between total stand volume and the aboveground components of biomass (i.e. stem, foliage and branch) at the stand level, 2. To investigate how the relationships between total stand volume and aboveground component biomass change with stand characteristics (i.e. initial plant spacing, site index and age), 3. To determine if the ratio between component biomasses is affected by these stand characteristics, and 4. To apply regression analysis to explore the relationship between biomass and volume with and without selected stand characteristics, and also the ratios between component biomasses. Chapter 2 explores the relationships, trends and possible ranges in coastal Douglas-fir biomass. Chapter 3 evaluates whether the knowledge of stand characteristics other than volume as predictor variables would improve stand-level biomass prediction in regression analysis. Concluding remarks are given in Chapter 4. 2 2. RELATIONSHIPS BETWEEN STAND BIOMASS AND SELECTED STAND CHARACTERISTICS 2.1 INTRODUCTION The purpose of this chapter is to investigate the relationship between total stand volume and aboveground tree biomass components (stem, branches and foliage) with selected stand characteristics such as age, site quality, and initial spacing. The ratios between these biomass components are also examined with respect to the above stand characteristics. A thorough understanding of stand biomass dynamics allows for better biomass predictions. 2.2 BACKGROUND 2.2.1 Biomass and Volume Both stand biomass and stand volume are measures of how much forests is in an area. Biomass and volume differ in their units and uses. Biomass is a measure of mass and is usually expressed in kilograms for a tree or tonnes for a stand. Volume is a measure of space occupied by the fibre in a tree, or from all the trees on a unit area, expressed in cubic metres (The New Oxford Dictionary of English 1998, Davis et al. 2001). Typically, volume is important in quantifying the commercial material that can be extracted from the boles of trees in a stand. On the other hand, biomass is relatively easier to use in quantifying the amount of foliage and branches. For the aboveground parts of a tree, biomass is usually broken into three components: stem, branches, and foliage. Stand volume is often used in predicting stand biomass, because the two are correlated and volume is frequently estimated in forest inventories. Volume to biomass relationships are particularly important in aggregating and predicting biomass for stands of various forest types, ages, stocking, and site productivity in regional and national biomass-carbon budgets (Birdsey 1992, Alexeyev and Birdsey 1998, Fang et al. 1998, Kurz et al. 2002). 3 Therefore, the three aboveground biomass components will be discussed with respect to the following stand characteristics: age, site quality, initial spacing, and total stand volume. 2.2.1 Stem Biomass Total stem biomass has two components: stem wood and stem bark. In this thesis, stem biomass refers to total stem biomass. Stem biomass is a critical component in biomass estimation because it is the largest component in total aboveground tree biomass. Stem biomass is often estimated by multiplying volume by relative density (oven-dry weight/ oven-dry volume). Although the relative density of stem wood and stem bark usually differs in most species, the relative densities of the two components are similar for coastal Douglas-fir (Haygreen and Bowyer 1989). Nonetheless, most researchers report biomass equations for these components separately (e.g. Table 1, page 9). In terms of the influence of stand characteristics on stem biomass, past research has concentrated on the impacts of spacing, thinning and fertilization on wood quality (i.e. specific gravity1) or biomass distribution (Brix 1981, Briggs and Smith 1985, Barclay et al. 1986, Fabris 2000). Initial spacing has little effect on specific gravity in young stands and thinning tends to lower specific gravity in older stands, except in dry sites (Briggs and Smith 1985). With the exception of very poor sites, fertilization causes specific gravity to decrease for a few years before recovering (Heilman 1961, Briggs and Smith 1985). Trees that have been thinned and/or fertilized have proportionally less aboveground biomass in stem biomass (Barclay et al. 1986). When trees were fertilized, there was proportionally more aboveground biomass as foliage and live branches but when the trees were thinned, there was no change in the proportions in foliage and branches (Barclay et al. 1986). Specific gravity is the ratio of the density of material to the density of water yet numerically identical to relative density. The latter is true when assuming the use of distilled water at 4°C because the density of water would be lg/ cm3 (Haygreen and Boyer 1989). 4 2.2.2 Branch Biomass Most research on branch biomass has been conducted in the context of tree biomass distribution or branch production (Whittaker 1965, Whittaker et al. 1974, Barclay et al. 1985). The proportion of aboveground tree biomass in branch biomass generally increases with tree diameter but may be dependent on species. For example, this trend was shown for Abies balsamea (L.) M i l l , for diameters up to 25 cm (Baskerville 1965a) and broadleaf-deciduous trees (e.g. Betula alleghaniensis Britt., Fagus grandifolia Ehrh., Acer saccharum Marsh.) for diameters up to 60cm (Whittaker et al. 1974). Cole and Dice (1969) predicted over the 26 cm tree diameter range, the proportion of total tree biomass in above and belowground biomass as live branches to decline slightly, plateau, then increase slightly. The live branch proportions for the entire diameter range were between five and ten percent of the total tree biomass. Furthermore, Johansson (1999) predicted similar trends for Picea abies (L.) Karst. but estimated a slight decline in larger diameters (i.e. 25 cm dbh). Branch biomass also increased with site quality (Keyes and Grier 1981). Ovington (1957) found branch biomass increased then reached a steady state over time in Pinus sylvestris L . forests. Most research literature explains branch biomass trends over tree diameter, but there seems to be a lack of literature on the stand-level branch biomass over age. Biomass equations for branches are often separated into live and dead components (Grier and Logan 1977, Gholz et al. 1979, Standish et al. 1985). However, Kurucz (1969) and Kurz (1989) developed equations for only live branches; it is unclear whether dead branches were included in the equations of Shaw (1979). Branch biomass equations have also been developed for branch diameter class (Kurucz 1969, Brown 1978, Standish et al. 1985). 5 2.2.3 Foliage Biomass Much biomass research has focused on foliage biomass because primary photosynthesis occurs in foliage. Foliage biomass provides an indication of primary production and the amount of photosynthetic material that may be allocated to various parts of a tree. Therefore, most references on the effects of stand characteristics on biomass are in relation to foliage biomass (Satoo 1962, Baskerville 1965a, Keyes and Grier 1981, Satoo andMadgwick 1982). The question asked by many ecologists is: what happens to the amount of foliar biomass after the maximum foliar biomass is reached? According to Satoo and Madgwick (1982), there are three potential foliar biomass trends over time: 1) the maximum foliage is maintained over time, 2) after the peak, the foliage decreases slightly then plateaus, and 3) once the maximum occurs, the foliage decreases over time (Figure 1). Examples of these different foliar biomass trends over time were discussed by Satoo and Madgwick (1982). However, specific foliar biomass trends for Douglas-fir were not found in the literature. Foliage Biomass (t/ha) Stand Age (years) Figure 1: Possible foliar biomass trends over time. Most studies suggest greater foliage accumulation in more productive stands (Koerper and Richardson 1979, Keyes and Grier 1981, Satoo and Madgwick 1982, Kurz 1989). For example, when Keyes and Grier (1981) investigated 40-year-old Douglas-fir stands, they found aboveground net production to be 13.7 t/ha on a high productive site and 7.3 t/ha on a low productive site. Kurz (1989) also found that aboveground biomass increased with increasing site indices. However, such a trend may be species-specific or as Baskerville (1965a) and Brown (1978) pointed out, differences in biomass may be attributed to species tolerance. The influence of stand density on foliage biomass may be better explained by relative stand density2 rather than absolute stand density3. In a review of several studies that examined different species, Satoo and Madgwick (1982) found that those studies that found leaf biomass independent of stand density were based on experimental plots that had different spacing and thinning regimes, but high relative stand densities. On.the other hand, studies that found increasing leaf biomass with corresponding increases in stand densities were from timber production forests having widely varying relative stand densities. They concluded that foliage biomass is affected by relative stand density rather than absolute stand density. Over relative stand densities, biomass increases at low relative stand densities and shows no relationship at high relative stand densities. 2.2.4 Tree-level Biomass Equations A literature search of Douglas-fir biomass equations was conducted. Equations were described here if they: 1) Were based on sample trees that represented at least a range of 50 cm diameter outside bark at breast height (1.3 m at the point of germination or high side of bole, dbh); 2) Were fitted equations for coastal Douglas-fir stands from British Columbia, Oregon or Washington; 2 The relative stand density measure, based on the Reineke's stand density index (1933), is the ratio of the actual number of trees to the expected maximum number of trees based on the mean diameter in the stand (Satoo and Madgwick 1982). 3 Absolute stand density is the actual number of trees per unit area. 3) Were based on unmanaged stands (i.e. equations developed to examine the effects of fertilization or thinning regimes were not selected); and 4) Were based on samples from more than one location or plot. Particular emphasis was placed on equations that included independent variables other than dbh. 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C J C JZ o o o c c c CO CO CO i _ CQ CQ CQ co co CO CM CO T t CD co CD T t CM CM co T t CO 0 0 LO CD LO d d d CO 0 0 CO co i LO co co CD T t n 1 II CM IX o IX T t CO LO CD CO co I * CM I*" CM CO V <° LO II co l x D a a CM CM CM 5 5 5 o o o CD -i- CD N CO O) CD CD CO ID N T t O O o o o o d d >- >- II II > > (D aT oo oo CD CD ZZ- zz O CD N N 3 CD X. ZZ-CO oo CM CM CM LEGEND N = sample size used to fit equations x = mean value D = diameter at breast height (cm) H = total tree height (m) V = volume inside bark (m3) FV = foliar volume (m3) SA = bole surface area (m2) CL - crown length (m) BRSA = branch surface area (m2) CA = crown area (2D projection on ground) (m2) BA = basal area pow (x, y) is x raised to the power y GSI = growing space index where a GSI of 100 represents no competition and a GSI of 0 is maximum competition with neighbouring trees (Lin 1974). GSI is the cumulative influence of one tree in each of the four quadrants surrounding it: 4 GSI = I GSI; i = l where G S I j : if 6 < 2.15° then GSL=25; if 9 > 5.25° then G S I i = 0; if 2.15°< 9 < 5.25°then GSIj = 25 - 8.0645(9 - 2.15)* Dj + Pi 2Dj " where Dj = diameter of the i t h competing tree (cm), Dj = diameter of the j t h subject tree (cm), and 9 is the angle between two lines which, at breast height, connect the centre of the subject tree with the outside of the stem of the competing tree. The angle is a function of both the distance between subject tree and competitor and the dbh of the competitor (i.e. in each quadrant, the tree with the largest 9 is the competing tree) (Kurz 1989). CF = The correction factor is applied to log transformed data where CF is the antilog of one half the sample variance or antilog(MSE/2) (Baskerville 1972). Correction factors are only presented and used if the logarithmic bias has not been corrected for in the original equation. "Equations highlighted in bold are equations chosen for analyses in Chapters 2 and 3. bEquation uses imperial measurements. Biomass Y (lb), D (inches), H (ft), CW(ft). R 2 is based on imperial units but SEE reported here has been converted into kilograms (e.g. Kurucz 1969). 'Equations were fitted to the form, Biomass = aDb, using original data (Ter-Mikaelian and Korzukhin 1997). dEquations were developed from pooled data and the diameter range reported here is the diameter range for the pooled data but not necessarily for the data from which the regression was derived. The latter was not reported by Shaw (1979). Shaw (1970) also reported tree component biomass equations for stem wood, stem bark, and total stem. However, only total stem is reported and used here. eSite Class II - III approximates site index 30 - 36.6 m top height at 50 years (Dilworth 1973) Note: R2and SEE are the coefficient of determination and the standard error of the estimate, respectively and are related to the regression method used to fit the original parameters (i.e. equations in logarithmic form have a corresponding SEE in logarithmic units.) 13 Authors of the equations given in Table 1 developed equations for each of the biomass components (i.e. foliage, branches and stem) except for Goudie (2001), who only developed a foliage biomass equation. The purpose, methodology, and types of sampled trees in biomass research were very diverse; a brief description of the origins of the equations follows. Gholz et al. (1979) summarized biomass data and developed equations of trees, shrubs and herbs of western Washington and Oregon. The equations that were developed represented average plant biomass on diverse sites rather than particular areas or habitats. The Douglas-fir component biomass equations were derived from a collection of five data sets throughout the Pacific Northwest. Grier and Logan (1977) measured and compared biomass and production budgets of four diverse plant communities dominated by 450 year-old Douglas-fir. The four plant communities are warm-mesic Pseudotsuga-Rhododendron-Gaultheria, relative xeric Pseudotsuga-Castanopis, mesic Pseudotsuga-Rhodendron-Gaultheria, and cool-moist Pseudotsuga-Acer-Polystichum plant communities. Trees, understory vegetation, and root biomass were measured and modelled. The study was located in a small watershed in the western Cascade mountains of Oregon. The total aboveground tree biomass of the various communities ranged from 491.8 to 978.8 t/ha. Kurucz (1969) defined component functions for the simulation of forest fuels. At the University of British Columbia (BC) Malcolm Knapp Research Forest in Maple Ridge, B C , Kurucz sampled 23 Douglas-fir trees, one in each of the 5 cm (2 inch) diameter class from 2.5 to 122 cm (1 to 48 inches). To derive the crown regressions, Kurucz constructed hypothetical 14 crowns for 89 'model' trees using the crown component biomass from the 23 sampled trees extrapolated to the model trees. Crown component biomass regressions were then based on a total of 112 (i.e. sampled and modeled) trees. On Vancouver Island, BC, Kurz (1989) sampled six Douglas-fir stands varying from 32 to 70 years in age and from SI 20 to 41 m at 50 years (Bruce 1981). The stands were located in the Very Dry Maritime Coastal Western Hemlock subzone of the B C biogeoclimatic ecosystem classification (Krajina 1969, Pojar etal. 1987, Green etal. 1984) where the understory vegetation was dominated by Gaultheria shallon Pursh. and/or Mahonia nervosa (Pursh) Nutt. The corresponding aboveground biomass ranged from 135 to 573 t/ha. The objective of the study was to investigate foliage efficiency and carbon allocation above and belowground in relation to increasing site quality. Two types of equations were developed: one was based solely on dbh and others were based on both dbh and competition indices, where the growing space index (GSI) was the most powerful competition index predictor (See Table 1 legend, for a definition of GSI). Shaw (1979) assembled the biomass data produced by scientists associated with the International Biological Program Coniferous Biome, U.S. Forest Service, University of Washington, and University of British Columbia. The locations of the biomass data were not reported by Shaw but are assumed to be in BC and the Pacific Northwest of the United States. Because the variance in mass increased with increasing tree size, Shaw developed weighted least squares component biomass regressions with dbh and height as the independent variables. 15 The study by Standish et al. (1985) was an ENFOR (Energy from the FORest) project, part of a federal initiative to understand the possibility of using forest biomass as a nation's energy source. Biomass equations were developed for 22 commercial species including some hardwoods in BC. Sampling took place across B C except in the Queen Charlotte Islands, north coastal region, and the Peace River region. For each sampling site, data were also recorded for crown length and width, crown class (e.g. dominant, codominate or intermediate), location (e.g. latitude and longitude, elevation, slope position), and biogeoclimatic zone. The biomass equations however, make use of more easily available data such as dbh, height and volume. The foliage equation in TASS was developed by James Goudie (2001). Goudie sampled in close proximity to the Cowichan Lake Research Station on Vancouver Island in 1987 and 1988. Thirty-six trees (3 families, 3 replications, 4 trees per family-replication) were sampled from an abandoned 17-year-old progeny trial. These trees were estimated to be at a SI of about 44 m at 50 years (Bruce 1981). The other 18 sample trees ranged from 20 to 80 years-old and from SI 30 m to 35 m: seven of the 18 were completely open-grown trees. Ter-Mikaelian and Korzukhin (1997) compiled a comprehensive list of biomass equations for 65 North American tree species. A l l equations were in the form of M = aDh, where M was the oven-dry weight of the biomass component of a tree (kg), D was the dbh (cm), and a and b were regression parameters. Equations were presented in raw (uncorrected) form, but for equations from log-transformed data, correction factors were provided. Ter-Mikaelian and Korzukhin (1997) refitted the Gholz et al. (1979) equations. 16 2.2.5 Tree to Stand-Level Biomass Given a tree biomass equation, the biomass of a tree can be determined. However, without measuring all the trees in a stand, the estimation of stand-level biomass is less straightforward. Early studies have demonstrated that trees that are average for one characteristic (i.e. diameter) tend not to be average in other aspects (e.g. weight) (Baskerville 1965b, Attiwill and Ovington 1968, Madgwick 1973). Mean dimensions (e.g. height, diameter, basal area) do not necessary equate to mean canopy weight. Therefore, it is key to sample a variety of trees within a stand and to find the most accurate method of deriving stand estimates from tree-level data. Such tree-to-stand expansion methodologies include: 1. Every Tree Summation: a regression derived from a sample is used to estimate a population. The regression is applied to every tree in the population and the results are summed for the stand estimate. In this approach, the independent variables used in the regression are easily measured for single trees (Baskerville 1965b, Attiwill and Ovington 1968, Crow 1971). 2. Stand Table: the average biomass in each diameter class is multiplied by the number of trees in each diameter class and summed for the total stand biomass. The average biomass can be derived from a regression or weighed directly from sampling (Baskerville 1965b, Attiwill and Ovington 1968). 3. Average Weight: a few trees of average diameter or mean basal area are weighed. The average weight of these trees is multiplied by the number of trees in the stand4(Attiwill and Ovington 1968, Madgwick 1971). 4. Mean Tree Dimension: the mean diameter or the corresponding diameter of mean height, mean basal area, or mean volume is used as the independent variable in the regression. 4 Attiwill and Ovington (1968) used the average weights of four trees in a plot. For a stand, the sample of trees would have to be more. 17 The estimate from the regression is then multiplied by the number of trees in the stand (Baskerville 1965b, Crow 1971). Because the 'every tree summation method' (Method 1) includes the biomass of every tree size, assuming the biomass function is for the full range of tree sizes in the stand, it is theoretically superior to other 'averaging' methods. The 'every tree summation method' is frequently used as the reference for comparison'with other methods (Baskerville 1965b, Attiwill and Ovington 1968, Crow 1971). Baskerville (1965b) found that the biomass estimate derived from using a stand table (Method 2), and the corresponding diameter based on the average volume in a regression (Method 4) resulted in biomass estimates within ten percent of the tree summation method and could be used if rough estimates sufficed. He also concluded that for tolerant conifers, the use of corresponding diameters based on mean dimensions other than volume (Method 4) can lead to gross errors and that the error would be less in intolerant species where the range of tree sizes is usually much smaller than in stands of tolerant species. The corresponding diameter based on the mean basal area in a regression (Method 4) has often been used and has been found to be sufficiently accurate in even-aged, single-species stands (Crow 1971, Madgwick 1971). 2.3 METHODS To obtain stand-level biomass estimates, three things were necessary: 1) tree-level biomass equations, 2) stand level information, and 3) tree-to-stand methodologies. Tree-level biomass equations (Section 2.3.1) were applied to simulated stands generated by a growth and yield model (Section 2.3.2). Section 2.3.3 details the method of extrapolating from tree to stand level biomass estimates. 18 2.3.1 Criteria for Selecting Equations for Further Analysis From Table 1 on page 9, equations were chosen for this study if they represented: 1) reasonable estimates of biomass particularly with respect to biomass trends over time, 2) significantly different biomass weights for a given stand (hence indicating a possible range of biomass estimates), 3) different predictor (X) variables, and 4) wider ranges sampled. 2.3.2 Stand Data Description .-• . The provincial growth and yield model, the Tree and Stand Simulator (TASS, version 2.07.24) was used to investigate stand-level biomass and other stand variables across a range of site productivities, initial stand densities and ages. TASS is a biologically oriented, spatially explicit, individual tree model that is driven by height growth, branch extension and crown expansion of competing trees (Mitchell 1975, Mitchell and Cameron 1985, B C Ministry of Forests 2000). The crowns of individual trees expand or contract according to various internal growth processes (e.g. height growth), environmental factors (e.g. site quality), cultural practices (e.g. thinning and fertilization), and the physical restriction imposed by the crowns of competitors. The volume increment produced by the foliage is distributed over the bole annually and is accumulated to provide tree and stand statistics. Developed over the past 30 years, TASS has been calibrated to coastal Douglas-fir data from 885 plots or 4539 plot measurements on both managed and untreated natural stands in British Columbia, Alberta, the Pacific Northwest region of the United States, Europe, and New Zealand (Goudie 1997, Di Lucca 2000). TASS performs best within the sample data range of 100 years. TASS output is extrapolated after age 100, but still conforms to the provincial permanent sample plot data (Goudie 2002). Considering the financial resources and time needed to destructively sample many different stands for biomass, TASS is a cost-effective alternative source of stand data for evaluating biomass for different sites, densities and ages. 19 TASS was run to produce tree and stand data from pure, even-aged coastal Douglas-fir stands, in which the trees were randomly distributed. Stands generated from TASS had the following characteristics: • Site indices from 20 to 40 m at 5 m intervals (5 levels)5; • Initial spacing from 1.0 to 5.0 m at 0.5 m intervals (9 levels)6; and • Ages from 10 to 200 at 10-year intervals (20 ages). TASS provided a tree list for each of the 900 stands and a summary of stand-level information (Table 2). Additional stand statistics are provided in Appendix 1. The tree list contains statistics on each tree in each stand (Appendix 2). Table 2: Summary of stand statistics from TASS. Variable N Missing N Mean Standard Deviation Minimum Maximum Plant Spacing (m) 900 0 3 1.29 1 5 Site Index (height @ 50 years) 900 0 30 7.07 20 40 Age Class (years) 900 0 105 57.69 10 200 Stems/ha 900 0 884.99 1226.24 179 9787 Diameter at breast height (cm) 891 0 37.18 21.34 0.01 87.57 Height (m) 900 0 28.18 15.46 0.59 66.01 Crown Closure (%) 900 0 91.82 22.21 0.41 100 Basal Area (m2/ha) 878 22a 62.58 30.83 0.01 116.34 Total Volume (m3/ha) 859 41 a 812.66 562.52 1 2315 N is the number of stands. a In young stands where the basal area and total volume were nearly zero, these values were not reported. 5 Site index (SI) is the height at 50 years breast-height age (Bruce 1981). 6 Initial spacing (m) at a per hectare basis or initial stand densities (sph, stems per hectare) equates to: 1 m spacing = 10,000 sph; 2 m spacing = 2,500 sph; 3 m spacing = 1,111 sph; 4 m spacing = 625 sph and 5 m spacing = 400 sph. 20 2.3.3 Tree to Stand-Level Biomass Given the tree biomass equations and the tree and stand statistics at the stand level, there are a number of methods in extrapolating tree-level biomass (i.e. tree biomass equations) to stand-level biomass estimates (as discussed in Section 2.2.5). In my study, the 'every tree summation method' was chosen because computer technology makes it possible and it is widely accepted in the scientific community (Baskerville 1965b, Attiwill and Ovington 1968, Crow 1971). The tree statistics such as diameter and height from TASS were applied to various tree biomass equations (Section 2.2.4) and the biomass predicted from these equations for each tree in the stand were then summed for total stand biomass. Some young trees had missing values and were not included in the summation because the values were assumed to be close to zero and would not affect the total stand-level biomass. 2.3.4 Initial Spacing and Stand Density Although the main objective of this study was to investigate the biomass in stands of various initial plant spacing over time or total stand volume, it should be noted that for most natural forests, the initial plant spacing is unknown. On the other hand, stand density for natural stands can be measured but stand density declines over time. Stands of equal density have varying amounts of biomass because of factors such as age, site quality, and the cumulative effects on the trees from inter-tree competition. Initial spacing contributes to these differences in stem density and biomass over time; therefore, it is more meaningful to discuss and report stands of the same initial spacing, rather than absolute stand density, over time and total stand volume. As not to completely dismiss the biomass and stand density discussion, biomass over relative stand density were examined. As pointed out earlier, Satoo and Madgwick (1982) stated that foliage biomass might be better explained by relative density rather than absolute stand density. Therefore, Curtis's relative density was determined for each stand (Curtis et al. 1981): 21 where RD is relative density, B A is basal area per acre, and dq is quadratic mean stand diameter. Curtis's relative density was used rather than Reineke's stand density index (which was reported in Satoo and Madgwick 1982) because the former was easier to calculate (Daniel et al. 1979, Clutter etal. 1983). 2.4 RESULTS and DISCUSSION 2.4.1 Selection of Equations for Further Analyses For the comparison of stand biomass trends and estimates, the equations by Gholz et al. (1979) and Kurz (1989) were used for all biomass components. For additional analyses, the Grier and Logan (1977) and Goudie (2001) equations were used for foliage biomass, while the Grier and Logan (1977) equation was used for stem biomass. The choice of biomass equation is important because estimates and trends can differ tremendously as shown for foliage biomass over mean stand dbh in Figure 2 7. Because the first criterion for selecting equations for further analyses was for equations to have a reasonable biomass trend, equations by Standish et al. (1985) were not chosen. Both the foliage and branch equations by Standish et al. (1985) predicted conflicting and dramatically different trends compared to other equations. Foliage and branch equations based on dbh and height showed a positive parabolic trend over stand dbh; whereas the equations for the same components, but based on dbh and volume, showed a negative parabolic trend with negative biomass values over the same dbh range (Figure 2). The predicted stem biomass values by Standish et al. (1985) were similar to those predicted using the Gholz et al. (1979) equation, except for unusually high 7 With the exception of some young stands that had missing data, the results and graphs presented in this chapter represent the estimated biomass for all 900 stands. 22 values for young stands in the diameter-height based equation by Standish et al. (1985). Most of the biomass estimates predicted from Shaw's equations (1979) were between the biomass output predicted by equations from Gholz et al. (1979) and from Kurz (1989) for stem and branch biomass. The foliage equation yielded very high, unrealistic values for stands with volume over 1000 m /ha or for average stand diameters over 40 cm (Figure 2). The data set by which Gholz et al. (1979) derived their equations included the data from Grier and Logan (1977); therefore, the equations by Grier and Logan (1977) were not generally reported in this study. The equations by Kurucz (1969) were not used, because of the high standard error of the estimate associated with the foliage and branch regressions. The biomass values from the stem equation were extremely low compared to those of other equations and the results were deemed unrealistic. The equations by Ter-Mikaleian and Korzukhin (1997) were also not used because they were identical to the Gholz et al. (1979) equations, although the authors presented them in another equation form. Slightly lower stem biomass values were observed when compared to the Gholz et al. (1979) equations. From Kurz's equations (1989), dbh and growing space index rather than dbh as predictor variables were chosen. The former had a lower standard error of estimate and higher coefficient of determination, and the use of a competition index as another independent predictor allows for comparison with other dbh-only predictor equations. Tree-level biomass equations should be used within the range of the sampled data and site conditions upon which they were based. Although stand biomass is shown for the 200-year simulation period, results may be misleading because some equations (e.g. Kurz 1989 and Goudie 2001) were extrapolated far beyond their original extent. For example, in Figure 2, based on the sampling range, it is advisable to only compare equations up to 60 cm mean stand diameter. Perhaps what is most disturbing about the results is the lack of consistency in the 23 direction of trends over dbh (and time). In part, the model form of the tree equation has an impact on the pattern of biomass over dbh or time. In sections to follow, only selected equations, as explained in this section, were included in the discussion. 10 20 30 40 50 60 70 Stand Mean Diameter (cm) 80 90 100 Figure 2: Foliage biomass (t/ha) predicted by equations in Table 1 for stands varying in site productivity, age and initial spacing at different stand mean diameters (cm). 2.4.2 Range of Component Biomass Values In the absence of biomass measurements, I assumed that the chosen tree biomass equations provide reasonable stand biomass estimates. The total biomass in stem, branch, and foliage is predicted to be between 14 to 262 t/ha for a 30 year-old stand and 68 to 687 t/ha for a 60 year-old stand (Tables 3 and 4). The range in biomass, and hence the uncertainty in biomass estimates rises with age. The greater difference in biomass values in older stands reflects the greater heterogeneity in tree sizes or crown classes associated with stands that have had more time to develop. A l l minimum values reported in Table 3 and 4 were from stands of SI 20, 5 m 24 spacing. A l l maximum values were from stands in SI 40, 1 m spacing with three exceptions: i) the foliage value at age 30 for TASS [SI 20, 1 m spacing] ii) the foliage value at age 60 for Kurz (1989) [SI 30, 1 m spacing] and iii) the foliage value at 60 years for TASS [SI 40, 4 m spacing]. Consequently, for these immature to early mature stands, smaller amounts of stand biomass are produced in poor and widely spaced sites whereas greater biomass amounts can be found on rich and denser sites. Table 3: Range of biomass estimates (t/ha) by various equations at stand age 30. Age 30 Gholz et al. (1979) Kurz (1989) Grier & Logan (1977) Goudie (2001) All Equations Foliage Branch Stem Min Max 1.4 15.43 1.81 23.03 13.12 198.25 Min Max 1.42 10.53 I . 59 13.59 I I . 35 186.7 Min Max 0.77 9.3 1.15 16.07 16.05 236.54 Min Max 3.35 17.3 Min Max 0.77 17.3 I . 15 23.03 I I . 35 236.54 Dif ference 16.53 21.89 225.19 Total 16.33 236.71 14.36 210.8 17.97 261.91 3.35 17.3 14.36 261.91 247.55 T a b l e 4: R a n g e o f b i o m a s s e s t i m a t e s ( t / h a ) b y v a r i o u s e q u a t i o n s at s t a n d age 60. Age 60 Gholz et al. (1979) Kurz (1989) Grier & Logan (1977) Goudie (2001) All Equat ons Foliage Branch Stem Min Max 4.38 20.67 7.63 44.88 74.53 557.19 Min Max 5.08 12.33 4.41 29.12 58.59 565.3 Min Max 2.92 15.87 5.74 38.72 87.5 632.18 Min Max 9.74 20.31 Min Max 2.92 20.67 4.41 44.88 58.59 632.18 Dif ference 17.75 40.47 573.6 Total 86.54 622.74 68.08 606.8 96.16 686.77 9.74 20.31 68.08 686.77 618.69 Because the predicted biomass from the equations cannot be verified using stand measures, these were compared to stands and biomass from the literature (see Appendix 3). Scientists have different research objectives; consequently, there are many inconsistencies in the data reported, which makes biomass comparisons difficult. For example, some researchers may not: i) separate total canopy weight into foliage and branch components; 25 ii) state whether the stems per hectare reported have a diameter limit, in which the same portion of the stand was eliminated; iii) exclude minor species in the total stand biomass; or iv) have used the same tree-to-stand biomass methodologies. Nonetheless, the one stand datum that every researcher utilized was stand age. To determine what the range of biomass estimates is in the literature compared to those predicted from this study, the component biomass was plotted against the mean stand age (Figure 3). Over time, the range of reported biomass estimates is within the biomass range predicted by Gholz et al. (1979), but this may be because some of the studies that were compared were used in Gholz et al. (1979) equations. It should be noted that the tree equations, in which the predicted stand biomass from this study are based on, had been extrapolated beyond its sampling range. Therefore, the predicted stand biomass based on Kurz (1989) and Goudie (2001) may not predict well for ages over 80 years and for total stand volume over 750 m3/ha. Over total stand volume, no one equation chosen in my analysis seemed to capture all the biomass variation of the other studies reported in the literature (Figure 4). However, the biomass estimates from the other studies do fall mostly between the ranges predicted by the chosen equations, collectively. The chosen equations are therefore likely comparable with measures of stand biomass. 26 o s s o o LO o o tf o o CO o o o o tf) CO 0 >; CD D) < •a c ro CO O N r-N 3 o oo ON N o o T3 3 o 0 0 «5 ED •3 O • (eq /i) sseiuojg qouBja as o o LO o o tf o o 00 o o CNJ o o tf) ro CD >; CD D) < c ro to o o LO o o tf o o 00 o o CM o o tf) 1 -ro CD >. CD CJ) < 13 c ro to (ei| A) sseuio;g 86BIIOJ u (BLJ/I) sseiuo;g mats cn x c D . < 3 OJ - £ O ~o a S >> 3 CO £ > o 09 E _o 1/3 i s o .2 £ CD © SP i i 3 - a 00 M d ro &, E s I o s 1 CL) ro =s PQ bO ^ E CQ 2.4.3 Biomass versus Volume Specific gravity of wood has historically been used to determine stem biomass from volume. Because stem biomass makes up a large percentage of total aboveground biomass, biomass to volume ratios or expansion factors are often used to convert volume to total aboveground biomass (Birdsey 1992, Penner et al. 1997, Schroeder et al. 1997, Brown and Schroeder 1999). In general, stand stem and branch biomass would be expected to increase with total stand volume. Equations by Kurz (1989) and Goudie (2001) suggested stand foliage biomass increases to a maximum stand capacity before biomass declines with increasing volume (Figure 5). The Gholz et al. (1979) equation produced an overall increasing foliage biomass trend, but with slower foliage increase per increase in volume after 700 m /ha. This pattern corresponded to the plateaus in foliage biomass predicted by Kurz (1989) and Goudie (2001). Based on the sample data, all equations are likely comparable for stand volumes less than 1000 m3/ha. The Goudie (2001) biomass values predicted for 1 m spacing stands were unusually high at low volumes because of the lack of good data for very small trees and the functional form of the equation tended to yield large values (e.g. in Equation 18 on Table 1, page 11, the negative coefficient (-1.1092) for small heights can yield large values). For volumes greater than 1000 m /ha, the Kurz (1989) equation predicted exceptionally high stem biomass and this might be because the equation was extrapolated beyond the GSI and dbh ranges of the sampled data. Because the Kurz (1989) equation (Equation 7 on Table 1, page 9) contained a negative coefficient for GSI, large and older trees with a GSI of zero will consistently yield higher biomass estimates then trees that were free from competition. 29 2000 B 500 1000 1500 2000 2500 Total Volume (m 3/ha) 500 1000 1500 2000 2500 Total Volume (m 3/ ha) - K u r z (1989) O Gholz et al. (1979) Grier and Logan (1977) x Goudie (2001) 0 500 1000 1500 2000 2500 Total Volume (m 3 / ha) Figure 5: Relationship between stand-level component biomass (t/ha) and total stand volume (mVha) for A ) Stem biomass, B) Branch biomass, and C) Foliage biomass. 2.4.4 Biomass versus Age, Site Quality and Initial Spacing 2.4.4.1 Predicted biomass components To show the range of biomass estimates according to site quality and initial spacing, SI 20 and SI 40 at 1 m and 5 m spacing are shown on graphs throughout this chapter. More 30 productive sites had greater predicted biomass and for most component biomass values, denser stands had greater predicted biomass than more open stands of the equivalent site quality and age. Regardless of initial spacing, high SI stands are predicted to reach similar biomass per ha at older ages. Only small differences in the number of trees in a stand between the 1 m and 5 m spacing were noted after 120 years for higher SI stands (Figure 6). Therefore, it is possible that the biomass in stands of 5 m initial spacing, consisting of fewer, but larger trees, may approximate the biomass in initially 1 m spaced stands of greater numbers but smaller trees. On poorer sites, indicated by SI 20, the difference in the number of trees between the two spacing regimes was much greater (Figure 6). Most biomass components on poorer sites of 1 m and 5 m initial spacings; therefore, did not converge in estimate but may if predictions were greater than the 200-year time horizon. CO £ "55 E ~ 4000 50 100 150 Stand Age (years) 200 50 100 150 Stand Age (years) • SI 40, 5m Spacing X SI 20, 5m Spacing • SI 40, lm Spacing A SI 20, lm Spacing Figure 6: Number of trees in 1 m and 5 m spaced stands of SI 20 and 40 over time. Output from T A S S . Regardless of SI, stands of the same initial density followed the same pattern in terms of the relationship between stems per ha and predicted stem biomass. More productive sites self-thin faster, reaching a stand of fewer, but larger trees (i.e. more biomass) earlier than poorer 31 sites. Both predicted foliage and branch biomass followed a similar trend as that shown in Figure 7 for predicted stem biomass. • 1m Space • 2m Space 3m Space x 4m Space X 5m Space 0 2000 4000 6000 8000 10000 Stems/ha Figure 7: Stem biomass (t/ha) versus stand density (stems/ha). Five different initial plant spacing for all site indices are represented and are derived from the Gholz et al. (1979) equations. 2.4.4.2 Predicted stem biomass For a given age, stem biomass predictions differed with spacings but greater differences were attributed to site quality, particularly in older stands (Figure 8). If equations by Gholz et al. (1979) and Kurz (1989) represented the range of possible biomass predictions at age 60, the average stem biomass for all spacings at SI 40 would be four times greater than the average of all spacings at SI 20. Predicted bole biomass increased with relative stand densities especially at high relative densities (Figure 9). For a given age, the effect of similar biomass amounts across different relative stand densities is due to spacing, and increasing biomass amounts with corresponding increases in relative density is due to SI. There is more stem biomass in tighter spacings than wider spacings. This characteristic has also been documented by Harcombe et al. (1990) for Tsuga heterophylla (Raf.) Sarg. stands. 32 A B Stand Age (years) Stand Age (years) • SI 40, 5m Spacing • SI 40, lm Spacing X SI 20, 5m Spacing A SI 20, lm Spacing Figure 8: Stem biomass (t/ha) over time for A) Gholz et al. (1979) and B) Kurz (1989). 0 10 20 30 40 50 Relative Stand Density Figure 9: Relationship between stem biomass (t/ha) and relative stand density. Stands of all site indices, spacings, and ages are shown. 33 2.4.4.3 Predicted branch biomass Predicted branch biomass appears to increase over time, but on poor sites, biomass may reach a maximum stand potential (Figure 10)8. Predicted branch biomass also increased with relative stand density for the same reasons as stem biomass over relative stand density (Figure 11). Satoo and Madgwick (1982) cited a Pinus densiflora Sieb. et Zucc. study by Mori et al. (1969) where branch biomass increased with relative density, whereas no such effect was found by Kato (1968). The former study investigated a 55-year-old stand and the latter study, a 14-year-old stand. Without reference to the original literature, I surmise that Kato (1968) investigated stands where spacing effects would be more prevalent due to the stand age (i.e. 14), whereas Mori et al. (1969) observed site quality differences among his older stands. A B 0 50 100 150 200 0 50 100 150 200 Stand Age (years) Stand Age (years) • SI 40, 5m Spacing • SI 40, lm Spacing X SI 20, 5m Spacing A SI 20, 1 m Spacing Figure 10: Branch biomass (t/ha) over time for A) Gholz et al. (1979) and B) Kurz (1989). 8 This trend is true of all other branch equations in Table 1 except for Equation 21, which describes a negative parabolic curve. 34 80 70 ( ra 60 *3 in 50 ro iom 40 m o 30 c ro i_ CD 20 10 0 • Gholz et al. 1979 A Kurz 1989 10 20 30 40 Relative Stand Denisty 50 60 Figure 11: Relationship between branch biomass (t/ha) and relative stand density. Stands of all site indices, spacings, and ages are shown. 2.4.4.4 Predicted foliage biomass A l l three datasets (i.e. Gholz etal. 1979, Kurz 1989, and Goudie 2001) predicted an increase in foliage biomass with relative density (RD) for low relative densities, a conclusion supported by Satoo (1971) for Cryptomeria japonica (L. f.) D. Don (Figure 12). However, there were differences in foliage biomass output at high RD, depending on the equation applied. Foliage biomass derived from the Goudie (2001) and Kurz (1989) equations appeared either unaffected by RD or produced a biomass decline (i.e. Kurz 1989). Both the Gholz et al. (1979) and Kurz (1989) foliage biomass outputs tended to be less dependent on SI and more dependent on spacing. On the other hand, the spread of foliage biomass predicted by Goudie (2001) over RD was dependent on both SI and initial spacing. 35 • Goudie (2001) 0 10 20 30 40 50 60 Relative Density Figure 12: Relationship between foliage biomass (t/ha) and relative stand density. Stands of all site indices, spacings, and ages are shown. More uncertainty was involved with foliage biomass predictions compared to the other biomass components. In comparing foliage biomass trends from four different equations (Figure 13) to those observed in other stands (Figure 1, page 6), it appears that Douglas-fir foliage biomass reaches either a maximum steady state or a peak-decline-then steady state. As indicated before, equations are most comparable up to a stand age of 60 years. Beyond this age range, the Kurz (1989) equation predicted less foliage biomass for high SI stands than low SI stands. A possible reason is the positive coefficient on GSI in Equation 16 in Table 1, page 10, would yield low biomass values for the high competition trees found in older stands. Based on the sample data, the Gholz et al. (1979) equation is likely to be the most robust within the range of stand conditions presented in Figure 13. 36 B 50 100 150 Stand Age (years) D 50 100 150 Stand Age (years) 200 50 100 Stand Age (years) 100 Stand Age (years) 200 SI 40, 5m Spacing • SI 40, lm Spacing X SI 20, 5m Spacing A SI 20, lm Spacing Figure 13: Foliage biomass (t/ha) over time for A) Gholz et al. (1979), B) Grier and Logan (1977), C) Kurz (1989), and D) TASS. Stand foliage biomass may decline during stand break-up when more biomass is lost from a few large trees than is compensated for by small regenerating trees. In TASS, stand break-up is not modeled, but crown closure is modelled. At least 95 percent crown closure is expected for all the stands at the end of the 200-year simulation period. Crown closure in TASS has not been thoroughly tested against sampled data, but is suspected to be biased towards greater closure, because it models crowns as circles rather than jagged edges (Polsson, 2002). 37 TASS only 'grows' or 'kills' trees, but no new trees were added in the model over time to represent regeneration during stand break-up. In stands older than 100 years, stem mortality is still occurring, but at a slower rate (Figure 6, page 31). It is difficult to tell whether this mortality would contribute significantly to the overall decline in foliage biomass in some equations. Assuming that most of the tree mortality is in suppressed trees rather than in codominant trees, the foliage biomass is not likely to vary. It is also believed that foliage biomass remains constant over time, because trees will attempt to utilize all the available space to grow and, once maximum foliage is reached, the crowns 'lift'. Annual foliage production replaces older foliage falling onto the forest floor. Franklin and Waring (1979) attributed the large biomass in older Douglas-firs in the Pacific Northwest to the longevity of the species, the ability to accumulate and maintain large amounts of foliage, and the ability to sustain height growth. Compared to other ecosystem types, there are also relatively fewer insect outbreaks and lower fire frequencies where coastal Douglas-firs grow (Franklin and Waring 1979). In a study on 400 year-old coastal Douglas-fir, Ishii and Ford (2001) found epicormic shoot production maintained shoots and foliage of these old trees after height growth and crown expansion had stopped. They found epicormic shoots produced ten percent to nearly 50 percent of shoots and foliage of branches. Furthermore, epicormic branches contributed to increased crown depth (Ishii and Wilson 2001). At an individual tree level, foliage biomass may be maintained by epicormic shoots in old trees, but during windy days, small vegetated twigs may also be removed. At a stand level, it is difficult to determine whether foliage biomass would be maintained. On more productive sites, the loss of a few big trees may be significant and the trees may not be able to close the gaps left from wind-thrown trees or it may take a considerable amount of time. 38 2.4.5 Biomass/ Volume Ratios versus Age, Site Quality and Initial Spacing For all biomass component to volume ratios, the difference in biomass for a given volume is attributed more to spacing than SI. Poor sites reached similar predicted biomass to volume ratios as richer sites, but at later volumes. However, at a given age, biomass to volume ratios were higher for poor sites. At a certain total volume and spacing, the biomass to volume ratios of poor stands were slightly higher than the ratios for rich stands. 2.4.5.1 Stem Biomass/"Volume Ratios Wider spaced stands had greater stem biomass to volume ratios for any given volume, except in cases of low volume (Figure 14). In this case, the ratios for dense spacing were similar or slightly higher than wider spacing. The reason wider spaced stands have proportionally greater stem biomass to volume ratios is likely attributed to age. For similar stand volumes, stands containing wider spaced trees were older than those of closer spaced trees. Older trees have proportionally more mature wood than juvenile wood. Moreover, Fabris (2000) hypothesized that although wider spaced trees have proportionally more juvenile wood than mature wood during early development, it is conceivable for this proportion to decrease over time to a point even lower than the proportion in tighter spacings. The specific gravity of wood or relative density in mature wood (0.46-0.49) is greater than that in juvenile wood (0.39-0.46). As a result, widely spaced trees with more mature wood may have a higher relative density than tightly spaced trees for a given volume (Jozsa and Middleton 1994). 39 A B Total Volume (m 3 / ha) Total Volume (m 3 / ha) • SI 40, 5m Spacing • SI 40, lm Spacing X SI 20, 5m Spacing A SI 20, lm Spacing Figure 14: Stem biomass over total volume for A) Gholz et al. (1979) and B) Kurz (1989). In young stands where the bole is primarily juvenile wood, the relative density of wood is expected to be higher in the tighter spaced trees (Briggs and Smith 1985). Therefore, it is possible that at young ages, denser stands may have greater biomass : volume ratios. In my study, only the Kurz (1989) equation predicted more biomass per unit volume for the 1 m spacing compared to the 5 m spacing at SI 20 (not visible from Figure 14). The transition from juvenile wood to mature wood occurs when the stand is about 10 to 30 years (Jozsa and Middleton 1994). Unfortunately, the transition of juvenile to mature wood for different spacing and SI has not been thoroughly researched. Since data was missing for stands younger than 20 years old, no meaningful conclusion can be drawn. 2.4.5.2 Branch Biomass/ Volume Ratios Branch biomass to volume ratio patterns were similar to those of stem biomass to volume ratio patterns. For a given volume or age, denser stands had lower branch biomass to volume ratios, but the ratio difference between tighter and wider spacings was small (Figure 15). It is conceivable that widely spaced trees have larger crowns, and consequently, more branch 40 biomass, and a few large trees, collectively, have marginally more branch biomass for a given volume than many, small trees. A B • SI 40, 5m Spacing • SI 40, lm Spacing X SI 20, 5m Spacing A SI 20, lm Spacing Figure 15: Relationship between branch biomass (tf ha) and total stand volume (m3/ha) for A) Gholz et al. (1979) and B) Kurz (1989). 2.4.5.3 Foliage Biomass/ Volume Ratios In contrast to stem and branch biomass, denser stands had more predicted foliage biomass for a given volume or age (Figure 16). This difference was quite significant for Gholz et al. (1979) and Kurz (1989). For a given volume, younger and denser stands were being compared to older and more open stands. It is expected that in older and more open stands that the foliage biomass is maintained, but the stand volume continues to increase. Therefore, these stands tended to have a lower predicted foliage biomass to volume ratio. Younger stands tended to have proportionally more predicted foliage biomass compared to stem biomass or volume. 4 1 2.4.6 Component Biomass Ratios versus Age, Site Quality and Initial Spacing In using separate regression equations to predict each biomass component, biomass additivity is a concern where components added separately may not equal to total biomass. A total aboveground biomass equation was not available from the study by Kurz (1989) or Gholz et al. (1979). It is possible to assume that total biomass is the sum of the leaf, branch and stem biomass components predicted from the published equations. However, components add up to the total if: 1) exactly the same model is fitted for all of the components and total, 2) the transformation is linear in scale when transformation is used on the dependent variable, and 3) all equations are fitted from the same observations (Kozak 1970). The Gholz et al. (1979) equations were not fitted to the same sample size and the Kurz (1989) equations differed in model form for stem bark. To circumvent this problem, component biomass ratios may be determined over stem biomass instead of total biomass. Component biomass ratios are referred to the components (e.g. foliage and branch biomass) over total biomass or stem biomass. The component biomass ratio also includes stem biomass over total biomass. Both component biomass ratios are used in this study, because the ratio over total biomass would permit all three biomass components to be compared. A ratio over stem biomass may be more practical to use; this method has been utilized in a recent carbon study of BC forests (Kurz et al. 2002). Both component biomass ratios produced the same trends but differed in the absolute values; this result is expected since the majority of the total biomass was comprised of stem biomass. Over time, predicted stem biomass increase and predicted branch and foliage biomass decrease proportionally to total biomass to a point that likely corresponds to stand closure (Figure 17). At this point, the portions of all component biomasses to total biomass are almost 43 constant, but predicted foliage and branch biomass proportions are still slightly declining and stem biomass proportions slightly increasing. <f> cc E o in c cu c o a. E o O cu O) CO c cu o cu CL 70 60 50 40 30 20 10 A Percentage of Stem in Total Biomass • Percentage of Branches in Total Biomass o Percentage of Foliage in Total Biomass ^ i i i i n i i n i i i i i i l 50 100 150 Stand A g e (years) 200 Figure 17: Foliage, branch and stem proportions to total biomass for all spacing and SI stands over time for Gholz et al. (1979) equations. 2.4.6.1 Ratios of stem biomass to total biomass For the same stand age, highly productive stands allocate more total aboveground biomass to stemwood (Figure 18). This is consistent with the findings of Keyes and Grier (1981) and Hatiya et al. (1966). For high SI stands, equations from Gholz et al. (1979) and Kurz (1989) suggested that the tighter spacing results in greater allocation to stem biomass or there is simply less space for the crowns to expand. In these stands, the trees may be competing more for light therefore allocating more stem biomass to height growth. 44 *- f i t * M~H~rH rr* 50 100 150 Stand Age (years) 200 B 100 T tf) tf> ra 90 -E o 80 -m 70 ~ o H 60 -0 tf) 50 -tf) CO E 40 -o CD 30 -E CD 20 -c/> c 10 -0 o -ra CC 0 -f-50 100 150 Stand Age (years) 200 SI 40, 5m Spacing SI 40, lm Spacing X SI 20, 5m Spacing SI 20, lm Spacing Figure 18: Percentage of stem biomass to total biomass over time for A) Gholz et al. (1979) and B) Kurz (1989). At low site quality, the dataset based on Gholz et al. (1979) equations predicted the 5 m spaced stand to have proportionally more stem biomass than the 1 m spaced stand, whereas the Kurz (1989) based dataset predicted the 1 m spaced stand to have proportionally more stem biomass than the 5 m spaced stand. Both equations predicted a similar amount of stem biomass but Gholz et al. (1979) predicted much more foliage and branch biomass than Kurz (1989) for the 1 m spacing compared to the 5 m spacing at SI 20, thus contributing to these differences. On poor sites, it is possible for the tighter spacing to have proportionally more stem biomass, because of the allocation to height growth due to light competition. However, if nutrients are limiting (as they may be on a poor site) then compared to the tightly spaced trees, wider spaced trees may be able to allocate more biomass to stemwood. Although published research was found that compared biomass for site productivities (Koerper and Richardson 1980, Keyes and Grier 1981), little was found on spacing effects. 45 2.4.6.2 Ratios of foliage and branch biomass to total biomass Compared to high SI stands, the equations by Gholz.et al. (1979) and Kurz (1989) showed low SI stands distribute more of their total aboveground biomass to foliage and branch biomass than stem biomass (Figures 19 and 20). These findings were consistent with those by Hatiya et al. (1966), Koerper and Richardson (1980), and Keyes and Grier (1981). Similar results were seen with leaf and branch biomass over stem biomass (Appendices 4 and 5). The predicted ratio of branch to stem biomass declined over time, which was also evident in studies by Ovington (1957) and Whittaker (1962). With the same SI and age, the Gholz et al. (1979) and Kurz (1989) equations produced different ratio results for closer and wider spacing. I would expect the widely spaced trees to have proportionally more foliage and branch biomass, since larger trees tend to have proportionally more foliage and branches compared to the stem (i.e. the trends from Kurz 1989). Findings by Baskerville (1965a) for Abies balsamea (L.) M i l l , also support this idea. Further research would be required to address the questions of biomass distribution in stands from a wide range of spacings. 46 B cn cn CO E g in CD OI CO o o co DC 50 100 150 Stand Age (years) 200 cc CC 50 100 150 Stand Age (years) 200 SI 40, 5m Spacing SI 40, lm Spacing X SI 20, 5m Spacing SI 20, lm Spacing Figure 19: Percentage of foliage biomass in total biomass over time for A ) Gholz et al. (1979) and B) Kurz (1989). Figure 20: Percentage of branch biomass in total biomass over time for A ) Gholz et al. (1979) and B) Kurz (1989). 47 2.4.7 Component Biomass Ratios versus Volume When plotted against total stand volume, both Gholz et al. (1979) and Kurz (1989) equations predicted that 5 m spaced stands attain proportionally more stem biomass of the total aboveground tree biomass than the 1 m spaced stands (Figure 21). Kurz (1989) predicted that 1 m spaced stands have proportionally more stem biomass initially, for stand volume less than 200 m3/ha. It is very possible that the closer spacing might have proportionally more stem biomass, particularly at such low volumes or early ages. For branch and foliage components, the reverse trend is true; both equations predict the 1 m spacing to have greater proportions over volume with the exception of the Kurz (1989) equation, which predicts the 5 m spacing to initially have greater proportions (Figures 22 and 23). Results are alike when component biomass ratios are over stem biomass (Appendices 6 and 7). A B Total Volume (m 3 / ha) T o t a i volume (m3/ha) • SI 40, 5m Spacing • SI 40, lm Spacing X SI 20, 5m Spacing A SI 20, lm Spacing Figure 21: Percentage of stem biomass in total biomass over total volume for A) Gholz et al. (1979) and B) Kurz (1989). 48 A B • SI 40, 5m Spacing • SI 40, lm Spacing X SI 20, 5m Spacing A SI 20, lm Spacing Figure 22: Percentage of foliage biomass in total biomass over total volume for A ) Gholz et al. (1979) and B) Kurz (1989). Figure 23: Percentage of branch biomass in total biomass over total volume for A ) Gholz et al. (1979) and B) Kurz (1989). 49 2.5 SUMMARY Results from this chapter showed that for a given age, differences in biomass could be attributed to site quality and initial spacing. Denser stands and richer sites had more predicted biomass over time. However, for a given stand volume, spacing effects were more influential on biomass components and component ratios than was site quality. Over volume, denser stands had more predicted foliage biomass and less predicted stem and branch biomass. Predicted biomass components and component ratios over volume differed with site productivity in that less productive stands reached similar biomass component or component ratios, as those in highly productive stands but at later ages. For a given stand volume, denser stands generally had greater predicted stem biomass, but less predicted foliage and branch biomass in total biomass. The trend analysis suggests measures of spacing or density and site productivity would be important in volume to biomass predictions. 50 3. PREDICTING STAND BIOMASS USING REGRESSION ANALYSES 3.1 INTRODUCTION In the previous chapter, trends and relationships between volume-biomass and other stand characteristics were discussed. In this chapter, the trends and relationships are predicted using regression equations. Although stand-level biomass may be obtained from tree plot data as described in Section 2.2.5, it is advantageous to develop stand biomass equations using stand variables because detailed tree level data for every stand are not available in forest inventories. 3.2 BACKGROUND There are three expressions of stand volume-biomass relationships: 1) volume-biomass functions: Y = aX, where Y is stand component biomass, a is a constant, and X is stand volume; 2) biomass expansion factors (BEF) or functions: BEF is the component biomass/ stand volume. A BEF function is the non-linear relationship between BEF and stand volume; and 3) proportion ratios or functions: Proportion ratio is the foliage or branch biomass/ stem biomass. A proportion ratio function is the non-linear relationship between the proportion ratio and stem biomass. The relationship between stem volume and stem biomass can be assumed linear; it differs mostly by a constant, namely the specific gravity of wood. Therefore, biomass can be predicted from volume using a linear function (Fang et al. 1998). Volume-biomass may also be expressed as a ratio. It may take the form of a biomass expansion factor (component biomass over stand volume) or as a proportion ratio (component biomass over stem biomass). Early studies developed discrete stand biomass expansion factors (BEF) to estimate aboveground biomass 51 density (aboveground biomass in trees per unit area) (Birdsey 1992, Brown 1997). Later studies found BEF to decline as stand volume increased; therefore, continuous regression equations were developed to estimate BEF for forest of any volume density (Schroeder et al. 1997, Brown and Schroeder 1999). The proportion ratio assumes stem biomass is calculated by multiplying the stem volume by the specific gravity of wood. Johnson and Sharpe (1982) estimated total stand biomass to stand stem biomass ratios for forests in Virginia by stand size class (i.e. sawtimber, pole timber, sapling/seedling, and nonstocked). Brown et al. (1989) developed similar ratios for stands in tropical forests, but found that the quadratic stand diameter (i.e. QSD, the diameter of a tree of average basal area) influenced the ratio. They found the proportion ratio is high and variable for small trees and a function between the proportion ratio and QSD was developed. At higher QSD, the ratio declines to a constant. Similar to the relationship between BEF and volume, the proportion ratio can vary depending on the stem biomass. Therefore, Kurz et al. (2002) created functions for the proportion of stand foliage and branches in stem biomass for all species collectively, by biogeoclimatic zones in BC. Although stand volume to biomass equations or ratios have been explored, little is known about the degree that stand volume accounts for the variation among biomass of different stands. Baskerville (1965a) found improved stand biomass predictions for Abies balsamea (L.) Mi l l , from volume per acre, compared to stems per acre, because stems per acre do not account for differences in tree sizes. However, stand density, site quality, and stand age may contribute to some of the variation among the relationships between stand volume and stand biomass. In terms of tree biomass equations, Feller (1992) discovered geographical and site-specific variation in Douglas-fir growth to significantly influence the parameters in biomass regression equations and this was especially noticeable in very poor sites. In a 18 year-old genetic test of Douglas-fir, 52 St. Clair (1993) developed separate tree biomass equations for 20 Douglas-fir families. St. Clair (1993) found the intercept of the tree crown biomass equations to differ, assuming equal slopes. This suggests that genetic variation is another stand factor to consider in biomass estimation. Satoo (1966) commented that the estimates from tree biomass equations derived from using diameters of trees sampled from a variety of stands may not be accurate, unless some measure of competition was also included in the tree biomass equation. Tree competition or crowding will affect the shape of the crown and as a result, a competition measure in the form of stems per hectare or some consideration of crown dimension may be useful variables to measure for the development of tree and stand-level biomass equations. The addition of crown variables to regression equations improved the prediction of tree foliage biomass estimated from branch diameter in coastal Douglas-fir (Kershaw et al. 1995) and crown components estimated from tree diameter in interior Douglas-fir {Pseudotsuga menziesii var. glauca (Mirb.) Franco) (Marshall and Wang 1995, Brown 1978). The inclusion of stand basal area (Monserud and Marshall 1999) and stems per hectare (Moeur 1981) also improved the tree foliage biomass equations for interior Douglas-fir. 3.3 METHODS Component stand biomass regressions were developed using stand-level biomass data derived from the tree biomass equations by Gholz et al. (1979), Grier and Logan (1977), Kurz (1989) and Goudie (2001), which were applied to TASS output data (See Section 2.3.2 for data description). Rationale for selecting these equations is found in Section 2.4.1. Although this approach constructs a model from another model, it was used to gain understanding on how 53 stand variables may affect biomass prediction at the stand-level. It is assumed these stand-level biomass data are representative of real stands. Three types of stand biomass models, which differ with predictor variables, were created for each dataset derived from the chosen component tree biomass equation: Model 1: a regression predicted from stand volume (volume/ha), Model 2: a regression predicted from inventory data (i.e. volume/ha, SI, mean stand age, and mean stand height), and Model 3: a regression predicted from all variables available from TASS (see Appendix 1 for a list of variables). Statistical analyses were conducted using SAS 8.1 (SAS Institute 2000). Prior to modelling, basic relationships between stand variables and biomass were examined through scatter plots and calculating Pearson's correlation coefficients (r). The regression analyses consisted of: 1) testing various transformations of the X and Y variables. Only 859 out of the 900 stands had total volume estimates (volume values were missing for young stands, which had volumes close to zero). Variables that did not exist for all 859 stands were not included in the modelling; 2) using stepwise, forward, backward and R 2 selection techniques (SAS Institute 2000); 3) eliminating predictor variables that were not significant to a probability level of 0.05; and 4) evaluating equations based on the coefficient of determination (R 2 or I2), standard error of estimate (SEE or SEE*), how well the equation met its assumptions in linear regression, residual plot analysis, and biological reasoning. For the comparison of the logarithmic Y values in original units, I 2 is the coefficient of determination defined as: 54 X(*-*>2 I 2 = l - - ^ i c ^ - j / ) 2 1=1 and the standard error of the estimate SEE* is: SEE*= 1 ^ ( y i _ 9 i ) 2 V n - m - l t r where n is the number of stands, m is the number of independent variables in the regression, y is the response variable, y is the mean of the response variable, y is the estimated value of the response variable, and all y values are in original units. To draw parallels to the trend analyses, the ratios estimated from the regression equations were plotted against the observed component biomass ratios. This allows for testing the model fit for individual component biomass functions used in proportion biomass ratios; values coinciding on a 1:1 line indicate a perfect fit. The observed was the ratio of stand foliage and branch biomass to stem biomass using the stand-level data originated from the TASS runs and using the tree biomass equations by Gholz et al. (1979) and Kurz (1989). The predicted ratio was derived from separate stand foliage, branch and stem biomass regression equations. The purpose of proportion biomass ratio functions is to predict biomass in foliage and branches from better known biomass components, such as stand-level stem biomass. Because component biomass regressions were provided, no actual regressions were created for the biomass proportions. 55 3.4 RESULTS and DISCUSSION 3.4.1 Biomass and Volume Stand volume is a fairly good predictor of biomass, particularly for stem and branch biomass as shown by the high R 2 (or I2) and low SEE (or SEE*) (Table 5). Volume is also highly correlated with both stem and branch biomass for all datasets based on the various tree biomass equations (r > 0.96, p = 0.0001) (Tables 6 and 7). Depending on the dataset from which biomass was derived, foliage biomass is generally poorly correlated with volume (Table 8). This may explain the low I for foliage biomass equations. A l l regression coefficients in Table 5 were significant (p < 0.0001) and all equations were based on a sample size of 859 stands. The residual plots of the equations showed a lack of fit or unequal variances; therefore, the regressions are likely biased. No confidence interval or F-test were calculated. Logarithmic transformations of biomass are often made to regressions used in biomass studies, because the shape of the regression is quite flexible while the increasing variance of mass with tree size is accounted for (Satoo and Madgwick 1982). Equation 31 (Table 5) was not log-transformed and had variances increasing with the Y variable, stem biomass. Such an equation may benefit from a weighted least squares regression analysis. Nevertheless, Equation 31 was kept, because the relationship between stem biomass and volume was strong (i.e. high R 2 , low SEE) and had better residual plots (i.e. less lack of fit) compared to models based on log-transformed data. By allowing the stem biomass to be in original units (kg/ha) for the Grier and Logan (1979) dataset, it is possible to have negative biomass values, using a linear unconstrained model. 56 CD '35 " C H 6 ro 00 ro 4= CD s > c ro M l C CO T3 O E C ro CZ) C O '& +-* ro c 3 co c/> P , <Z) . . . O . * .t; O LL CO _ CA 5 8 cr = a) ro = 1 •O « ^ " ro J Z CO Q O = H LU a> w Lu =Fj LU yj ^ CO ro £ o c o co o o CD t/j — 4) <U o > c -2 .2 T3 ro c > ro _ to § T3 al CD CO & H ro <+- CJ > N c S H • — ro S CO 5 I O 1 / 5 D ON . - . i n ro 0) Q- ro ^ ro s ^ CO co cu CA f t cu .2 i- "a O) 0 u 1 rr ^ c g (0 3 Ol LU s tf-NO Os CN •tf cn a s d + oo NO II Si oo e t~H Os CO CN ON r -ON s ON CN s NO i n OO d + oo Os p > i n ON cn o o o d + oo e N ON 00 p ON o CN ON NO CN cn • t f cn s o • t f ON —* o ON NO cn OO cn CN tf" o • t f CN oo 00 NO oo Os ON Os d d d ON NO >/-> i n '—1 oo • t f r~ d NO •tf- CN tf" i n > o cn CO i n o r -> SO NO o d I cn CN £ c ro be l i o Os • t f i n •tf > 00 oo NO > ' 00 CN cn O O o o + cn CN SO i n II 'a? OJO .5 "o P H o I o cn su « H cn ON Os m tf1 > CN r~ o oo d + r -CN •tf oo tf1 s CN SO NO o i n cn cn 00 CN CN Os 00 t-; SO • t f o i n CN i n CN cn cn • t f cn tf-oo i n CN > Os ,—i o o d I > i n CN o tf-o d + SO tf" > ON CN 1^  i n o o o d I CO 00 .2 P H CO bO .2 "o P H N cn cn os oo oo oo os <; O H tf-cn S s oo m tf-•tf a s CN" oo 00 o 00 d + •tf Os CN i n II o c ro •— PQ S - s <0 J= ON ^ a c • t f cn ON •tf o s b SO i n NO ON oo CN CN O Os • t f CN o O CN • 1 ' 1 CN • • • t f CN SO cn oo ^ « r~ NO • t f cn ON i n ON 00 Os SO Os Os d d d d d oo tf- CN s o O • t f tf- Os NO tf; i n 00 i n • t f - H T — H cn CN cn ^ > ^ s o cn Os s m cn o + tf-i n i n CN i n II 4= O c ro m SJ NO cn o o o d I Os 00 Os c 't/3 <U • — bJO <U •— U ro s o c 40 C o C H E o co 13 > i T3 C ro co CO •— C H -a CO CZ) CZ) C _o ro 3 c r . no ro czi ro % •« C 00 5 3 s £ H E ^ £ czi ro co •" o <u C X i <D ^ o S i ro S <» 5 c o o o ro c r c co o co "i: SN 0 3 ao 3 x: c r H co Table 6: Correlation matrix between stand-level stem biomass (derived from various equations) in kg and stand characteristics. A l l correlations are significant (p < 0.0001), except where otherwise noted. Number of Grier and Gholz et al. Kurz Stands Logan (1977) (1979) (1989) Total Volume (m3/ha) 859 0.99 0.99 0.97 Plant Spacing (m) 891 -0.10a -0.09a -0.05b Site Index (height @ 50 years) 891 0.57 0.57 0.61 Mean age (years) 891 0.73 0.72 0.66 Stems/ha 891 -0.41 -0.41 -0.37 Basal Area (m2/ha) 879 0.97 0.96 0.89 Diameter at breast height (cm) 891 0.95 0.95 0.94 Height (m) 891 0.97 0.98 0.96 Crown Closure (%) 891 0.49 0.48 0.38 Leaf Area Index 891 0.55 0.53 0.40 Height to the Crown (m) 891 0.97 0.97 0.97 Crown Length (m) 891 0.79 0.80 0.83 Percent of Crown Length 891 -0.46 -0.44 -0.31 in Height (%) Crown Width (m) 891 0.73 0.74 0.85 Crown Area 891 0.81 0.82 0.76 (2D projection on ground) (m2) a significant at the 0.01 probability level. b not significant at the 0.01 probability level. Table 7: Correlation matrix between stand-level branch biomass (derived from various equations) in kg and stand characteristics. A l l correlations are significant (p < 0.0001), except where otherwise noted. Number of Gholz et al. Kurz Stands (1979) (1989) Total Volume (m3/ha) 859 0.98 0.98 Plant Spacing (m) 891 -0.18 -0.12a Site Index (height @ 50 years) 891 0.51 0.51 Mean age (years) 891 0.74 0.75 Stems/ha 891 -0.38 -0.41 Basal Area (m2/ha) 879 0.99 0.99 Diameter at breast height (cm) 891 0.90 0.93 Height (m) 891 0.94 0.96 Crown Closure (%) 891 0.58 0.59 Leaf Area Index 891 0.64 0.64 Height to the Crown (m) 891 0.92 0.93 Crown Length (m) 891 0.71 0.76 Percent of Crown Length in 891 -0.59 -0.55 Height (%) Crown Width (m) 891 0.65 0.70 Crown Area 891 0.74 0.78 (2D projection on ground) (m2) a significant at the 0.01 probability level. 58 Table 8: Correlation matrix between foliage biomass (derived from various equations) in kg and stand characteristics. A l l correlations are significant (p < 0.0001), except where otherwise noted. Number Gholz et al. Kurz Goudie of Stands (1979) (1989) (2001) Total Volume (m^/ha) 859 0.87 0.08a 0.46 Plant Spacing (m) 891 -0.35 -0.37 -0.16 Site Index (height @ 50 years) 891 0.35 -0.19 0.33 Mean age (years) 891 0.70 0.37 0.42 Stems/ha 891 -0.26 -0.09a -0.07a Basal Area (m /ha) 879 0.97 0.41 0.65 Diameter at breast height (cm) 891 0.74 0.11a 0.52 Height (m) 891 0.81 0.18 0.56 Crown Closure (%) 891 0.72 0.75 0.82 Leaf Area Index 891 0.74 0.69 1.00 Height to the Crown (m) 891 0.75 -0.07a 0.47 Crown Length (m) 891 0.50 -0.11 0.40 Percent of Crown Length 891 -0.80 -0.86 -0.65 in Height (%) Crown Width (m) 891 0.43 -0.09a 0.37 Crown Area 891 0.53 -0.12 0.40 (2D projection on ground) (m2) a not significant at the 0.01 probability level. Most equations also had a lack of fit to the data and exhibited a curvilinear trend in residuals when plotted against the predicted value of biomass (e.g. Figure 24). In young stands, stand-level TASS data were limited and were at the extreme end of the sampling range for most biomass equations. Therefore, it is very possible for an over prediction in these stands (Figure 24). Because most mature to old-growth stands (e.g. in this analysis, 60 to 80 years-old and up to 200 years-old), have approximately the same foliage biomass, there tends to be a concentration at the higher predicted foliage values. For some studies, separate equations were developed for young versus mature trees, because younger stands appear to follow a different trend; most small diameter trees also tend to have a higher correlation between biomass and height rather than diameter (Brown 1978, Moeur 1981, Feller 1992). The problem with developing two separate equations based on two age ranges is at the point where the two age 59 ranges meet, a vertical gap in biomass may exist (i.e. there may be no smooth transition between the two age ranges). Therefore in my analysis, I developed equations for the entire age range. If merchantable stand volume was used instead of total stand volume in the regression, the regression tends to have a higher R 2 and lower SEE mainly because younger stands were eliminated from the data (n = 839). Stand foliage and branch biomass equations derived from Gholz et al. dataset (Equation 32 and 35 in Table 5) were slightly better predicted (i.e. higher I , lower SEE, and less lack of fit) with basal area/ha than from volume/ha. Basal area was strongly correlated with all three biomass components; the Pearson coefficient is higher for basal area than volume/ha for all foliage and branch biomass datasets predicted from the Kurz (1989) and Gholz et al. (1979) equations (Tables 7 and 8). „ 0.5 8 -2.5 0 2 4 6 8 10 Predicted Foliage Biomass (In units) Figure 24: Residual plot of stand foliage biomass from Equation 33, Table 5. 2 2 In Table 5, the R (or I ) of the same component biomass cannot be compared among the different regression equations because the data used to fit the regression equations were derived from different tree biomass equations. The standard deviation of the sample and the percent error of the mean are given to denote the variability of the sample and the sample mean, respectively. For example, among the stem biomass models, estimates observed using the dataset based on Kurz (1989) equations had more variability; consequently, this may have 60 resulted in the relatively high SEE. The dataset based on Kurz's (1989) equations had a wider range of biomass estimates because in the tree-level equations, there were two predictor variables, dbh and GSI, which gives a wider range of biomass estimates than with one predictor variable (e.g. dbh). 3.4.2 Biomass Using Volume and Selected Stand Characteristics as Predictors 3.4.2.1 Regressions based on inventory variables Regressions were also developed based on commonly available inventory variables namely, estimated total stand volume, mean stand height, stand age, and site index. In all regression equations, the stand height was significant (p < 0.0001) in explaining some of the variability in the biomass (Table 9). Compared to the other inventory variables, stand height was more likely to account for the variation in tree sizes of different stands. In most cases, age and SI were also helpful in explaining the variability around the regression line. Although the equations appear to have been significant (p < 0.0001), the equations did not fit well to the data, particularly for young stands. Except for the branch component equations (Equations 43 and 44), inventory-based equations were better than volume-based equations in Table 5 (i.e. larger R 2 or I 2 and lower SEE or SEE*). Both inventory-based branch equations showed that the addition of SI, age, and height did not improve the prediction. The R 2 values calculated for the logarithm of branch biomass using the inventory-based equations were higher than the volume-based equations; however, I values from branch biomass using the inventory-based equations were lower than the I 2 from the volume-based equations. The I 2 between the volume-based and the inventory-based were very similar. A reason for the lower I 2 value for the inventory-based equations is that these equations tended to have a greater lack of fit compared to the volume-based equations, particularly for large volumes. Nonetheless, the inventory-based stem and 61 foliage equations, as compared to the volume-based equations, explained a greater variability in biomass for a given stand volume (Figure 25). 62 c CD > c/5 S "O — £ = T3 rt rt ^ s & C CO -5 II O > to &. t>o E C rt •33 <*> 3 rt 1 ^ T3 -—' II CO ^ c rt X co rt 3 ^ -au c £ '33 .2 II CO c c £ O -S & 4-. s - a o £P S c« C/S ^> ~a E (D w 4-4 O CD =3 E 2 5 o- o o -a >^  S S-H rt £ " 3 > 00 rt a3 o rt o CD O C .2 rt > " r t g l CD C 3 C/3 CD rt o •3 c \ o O LU cc _ CO 3 8 a- = <D CC C •S ^ CU o c rror < Mea LU . 0 J C is? o * Ml HI LU LU CO w •2 c ~ CO 5" CO co a> > -a ro CD A =6 cu C o " £ cc 3 Oi LU "1 vn un O N O N CN VO <n r~ oo o + Tt Tt V) T t vd S s Tt CO O N O N O N PC Tt Tt vO O O d + O T t co cn O vo O T t O CN d d I + PC / -N CN 00 00 O . VO o o o o 2 N as CN cn O N vd II ? 2 oo o I co ro 3 00 m O N oo O N ON CN o IT) Tt vn o o Vn CN cn 00 d vn CN CN VO cn o o ON ON ON VO i n oo Tt d VO Tt CN Tt + < T t Os VO CN cn cn UO HH ffi 00 00 O + > o i n Tt + Vn I/O 00 ON I T ) CD 4J oo c n o c n o T t ~ cn >o ON O in s Tt VD T t vd i n ON ON 00 o ON cn «H Tt ON O ON VO vo T t 00 cn ON O Tt Tt + oo PC i OO '—\ CN r- i T t > r— T t PC T t CN > CN CN C o CN cn o o c o 0\ T t d d VO d o oo l I <n I d VO > < oo > I d o d CN + T t T t + < vn cn 00 T t CN vo VD T t O o O T t O o o o 00 o o CN o o d d d d II II S—^ ,—^  CD CD 00 W> .2 .S "o "o LL, N ON 00 p ON fed o s CN vO VO o m cn cn oo CN CN ON oo VO T t O l O <N wo o i cn cn T t cn CN CN OO CN T t T t Ov I I 1 1-H ^ 00 C O N C Tt o d + > CN vn o d + oo t N CN en od ll cn vo T t O o o d d PC s CN CD 00 .2 00 00 < E-i CN Tt c o o ON o U LL (0 _ CO § s Q) TO =1 T3 C TO 12 TO _j_ TO > ^ •i— d) CO Q CO o c , TO Is LU CP Ml S ILU QJ -C W CO CO w CN CC 9- TO tC 5 ^ «5 ?= .If <0 — ?! >-_^ o> a> OC c o TO 3 O l LU oo O N O N m co N O tf-CN o 1ft ON ON CN NO tf"' C O tf" co oo N O tf" co •tf-o oo ON NO • t f i a •tf CN — .•tf-O ro i n r \ o ~ O N O - d o • t f OO O + • t f r-•tf i/S II u e I* OH-CS C O faq ^ ^ O N !V 4= O N < o c ^ ro < N O 0 0 • t f o o o I < > )= o in tf-d + ro o ro oo N O oq (js O N O o c ro CQ + X oo ,00 • 00 o o d l < g j= i f IT) in t~~ CN ON tf" ON 0 0 d d 3 • t f • t f O N 0 0 ON c o CD OX) CD 1— 03 C CD C o o u 13 > J D i T3 C ro T3 CD '— CL O T3 CD ro ro T3 CD CD 3 l i Er ~ CD 0 0 C/3 0 0 < CD JS ro 6 o 'jS CD g u ft CD •4—' C*3 8 « c -5 CD O *o3 CN ^ c £ s ro -3 c o o ° \3 c ro —1 3 t/j ^ 5 CD O t*> ro 3 cr f-H <U CD 0 500 1000 1500 2000 2500 A Total \diire(rnVh^ B 0 500 1C00 1500 20CO 2500 Tefal vaLrrE(rn7 ha) predicted values from the equations O stand biomass Figure 25: Stem biomass versus total volume for A) volume-based Equation 29, and B) inventory-based Equation 37. 3.4.2.2 Regressions based on all variables If stand variables other than those commonly available are used (e.g. see Appendix 1), they might improve the estimates of the volume to biomass functions and improve the model fit. Al l regressions benefited from the addition of basal area per hectare and the incorporation of average stand crown dimensions (i.e. mean crown length or width in the stand) (Table 10). Stand basal area is a measure of stand density; therefore, in some Douglas-fir stands, density may influence the stand volume to biomass function. A l l regressions produced appeared to be significant (p < 0.0001), but all regressions still had a slight lack of fit. The model fit was better than those of the inventory-based regressions. Many variables presented in Appendix 1 were correlated to the component biomass. Nevertheless, these variables may not have been included in the regression equations, because a combination of other variables may be better related to the 65 stand volume to biomass function. From the same dataset, what is important to notice is the all variables-based equations (Table 10) were better in terms of R 2 , SEE and model fit than those of the volume-based equations (Table 5) and the inventory-based equations (Table 9). 66 "8 CO S CO ro <u e = 3 ro CO > ro E-i > •S S ^ •f CO CO Q o g 1- ro n CU LU 0) LU LU CO ro LU LU CO _cu Q- ro 'ro E ro S ^ CO ro . i f to — to > cu L , cn cu a> o tt =5 CD C o ro 3 LU O o o o r -cn oo CN O CN O cn N O ON ON 00 cn 00 o o o o O N i n •tf N O • t f + > 00 CN CN o o o o o O N CN I— o S O i n O N i n tf" • t f O N m CN N O 00 O N O N d N O r~ • t f i/n JS O H S. tf" • t f • t f O o o o o d I OH ~a o o oo N O ° < I CQ CN J3 cn O N C: ^ O N O cn - H ^ H II co "of O N I— O N e l tf1 cn r~- N O O N tf" cn N O c o d d I I [5 t o o JS a + H H + 0 0 00 > CN £ 8 oo o i n tf-m O N d + o •tf O N 00 N O II 1= co_ N O • t f +>C N cn C N r -o o o d o o ON 00 O N cn O N r~ cn >n N O cn 00 CN cn o O N 0 O m cn S O 00 O N O N O N d i n oo d CN i n + y < oo i n d 2 l q x o -tf I OS !£. D . O d CO Os CN •tf cn r~ N O cn > £ CN as CN oo cn •tf N O tf" + O N m o CN i n i n SO C N oo N O < CQ oo cn 00 p i n cn i n U N O C N SO I + Si co ns rt u O O —i O N o o o o I— cn oo cn i n >n Os 00 i n cn • t f O N O N Os OO O r--• t f Os C N o 00 so CN s o CN OO cn CN cn NO i n oo O N O •tf tf-JS O H O N + C N > § O N O 0 0 d oo ° O I o > I tf-"0 o N O O II d 'a? oo .2 "o PL, ad LH cn . o o o < A m a F- cn S O HH O N m o |~~ T-H O O N O N a 00 tf-+ & CQ CN V Os JS C3N i n cn NO O NO d > •tf o o o d + Os •tf cn p i n II CN OH + CN > o o O NO o o O cn d d CO oo .2 "o P H cn Os I— cn i n C N • t f S O N O N O i n Os i n O N Os d • t f Os I I < >-< so > CN "1= o o d o I d i o ^ 00 SO 00 cn o i— o cn o as d CO bO ro CQ c ' c oo •tf d I o P H N O N CO 00 CO 3 O N < ; W O H O N • t f o >n c o o co •a c 1|I 4-> CD (0 Q o c i_ co LU CU LU LU w-coH LU " LU (0 •2 Q- re co co 2 I f in — in >-cu 1" i - T3 O) CD » O 1 1 =5 CD c o 3 CO 3 OI LU i/o oo CN CO 00 oo I/O V O O N in in o o o o o CN N O T t CO CN uo T t O N o o o o o d + > + CO co >n Cti £ 8 <= oo O in o II O o c CN. o o d + < PP 00 O N Tt + H-l u m ^ O N < iio CN x .£ S OO 00 S CO CO ~ CN CO 0 O 00 H o o o d o ' + PP O N N O CO Tt Tt CO O N O N CN m in Tt d oo O N O N N O T t CN 1 V 00 | > O c o ^ Tt CN — S o NO O i CO rJ. I in o > ^ ON vrj CN 00 o o io o JZ o c cO u s CO CO N O CO o 3 CN in O N 00 O N <D l— <D I— <u J3 o '3 c CO c o P H E o o 13 > i c CO o s-C H T3 co oo cO o <D . « CO cfl CD _ „ o c3 c3 g , G O 3 H 03 co Cfl co H CO E 5 -8 E ^ o o o CO co ^ 3 2 H o cfl CO . „ c co . o CO CN • o c n ^ E ° E 3 CO «« o o o . E >, Cfl S..I  co 5-5 CO co > II ^ co E cfl CO w <- 22 a3 $0 E ^ CO PH -3 . „ CO ^ 6 *—I C/1 ^ CA C T 3 > c o « » E II u ? II CD cO - H ^ C > N II "2 J CO u « ^ II -5 « X E CD w -o CO C ^ co C^3 4H 2 '53 CO II b p '53 cfl C O cO < PQ r. C/3 v- cfl ° ON co in > 0 0 co - H ^ z 11 O <D E CD v—' C/5 C/3 s « 1^  E S ~ 5 3 O CO o - . > co b p j C "53 bj} -3 ^ oo NO II > 3.4.3 Component Biomass Ratios and Selected Stand Characteristics To obtain biomass components and component ratios, there are three possible methods with respect to modelling equations: 1) Biomass components only: The biomass components are fitted and the best equation is selected for each component. These equations are then used as component ratios (Method 1); 2) Biomass components and component ratios: the biomass components and the component ratios are both fitted separately (Method 2); or 3) Best fit for both biomass components and component ratios: equations that work well for both biomass components and component ratios are selected. This would require several equations to be fitted for each biomass component and testing the equations for estimating ratios (Method 3). In my analysis, Method 1 was applied because it was simpler, providing one set of equations, and the focus of the study was not on developing component ratios. The disadvantage of Method 1 is that the equations may not fit as well for the component ratios as in Method 2. Method 2 may provide the best equations for the biomass components and component ratios on their own, but these equations may not be compatible (i.e. the component ratio predicted from the component biomass equations may not be the same as the ratio predicted from the component ratio equations). Method 3 is recommended when both biomass components and component ratios are required, but it is also more difficult to apply. The proportions of foliage and branch biomass to stem biomass in a stand were calculated from the fitted equations found in Tables 5, 9 and 10. This section explores how well these estimated proportions fit with the TASS dataset and the Kurz (1989) and Gholz et al. (1979) 69 equations. Because the datasets using Kurz (1989) and Gholz et al. (1979) equations were different, they were not comparable. Compared to the component ratios derived from the Gholz et al. (1979) based dataset, the proportions using the inventory-based equations did not fit as well as using the volume-based and all variables-based equations (Figure 26). This trend may be reflected by the high SEE in the inventory-based branch equation (Equation 43, Table 9) and the relatively low variability in stand-level stem biomass. The low stand biomass variability may be attributed to the low number of predictor variables used in the Gholz et al. (1979) tree biomass equation. For the Kurz (1989) based dataset, the proportions using either the inventory-based or all variables-based equations had a better fit than the volume-based equation for branch biomass (Figure 27). However, the fit was about the same for the inventory-based and the all-variables based equations. The latter suggests that although the all-variables based equations can predict better than the inventory-based equations for individual component biomass, this may not be the case when these equations are used in predicting proportions. 70 A Observed Ratio of Branch to Stem Biomass (%) B Observed Ratio of Branch to Stem Biomass (%) 40 E o 55 35 TO CD 0 10 20 30 40 C Observed Ratio of Branch to Stem Biomass (%) Figure 26: Percentage of predicted branch biomass to predicted stem biomass using A) volume-based functions ( O ) , B) inventory-based functions ( • ) , and C) all variables-based functions ( A ) plotted against observed proportion biomass ratios from Gholz et al. (1979) equations. 71 0 5 10 15 A Observed Ratio of Branch to Stem Biomass (%) B 0 5 10 15 Observed Ratio of Branch to Stem Biomass (%) 0 5 10 15 Q Observed Ratio of Branch to Stem Biomass (%) Figure 27: Percentage of predicted branch biomass to predicted stem biomass using A) volume-based functions ( O ) , B) inventory-based functions ( • ) , and C) all variable-based functions ( A ) plotted against observed proportion biomass ratios from Kurz (1989) equations. When stand-level biomass ratios were predicted only by stand volume, the result was an average stand proportion for a given stand volume (Figures 28A and 29A). The all variables-based equations can help express most of the variability in proportion biomass for a given stand volume (Figures 28B and 29B). When the ratios of predicted biomass are plotted against volume, the results of the inventory-based equations fall between the variability explained by the volume-based and the all variables-based equations. 72 Figure 28: Percentage of predicted branch to predicted stem biomass (A) over total volume (m3/ha) for A) volume-based equations (Eqn. 29 and 35) and B) all variables-based equations (Eqn. 45 and 51). Original data is derived from Gholz et al. (1979) equations (O). Figure 29: Percentage of predicted branch to predicted stem biomass ( A ) over total volume (m3/ha) for A) volume-based equations (Eqn. 30 and 36) and B) all variables-based equations (Eqn. 46 and 52). Original data is derived from Kurz (1989) equations (O). 73 3.5 SUMMARY Results from this chapter showed total stand volume to be a strong predictor of biomass, except for foliage biomass. Although the effects of initial spacing on biomass were found by examining the trends and relationships, in the regression analysis, initial spacing was not found to be a significant predictor variable. Initial spacing was poorly correlated with biomass (Tables 6, 7 and 8). However, stand density effects were presented by other variables that were found to be significant in biomass prediction. The number of trees per hectare was a relevant predictor variable in some regression equations and stand basal area was a significant predictor variable in all component volume to biomass regression functions. Site index was only a significant predictor variable in some of the component biomass equations. Component biomass over stem biomass ratios were generally better predicted using all variables-based equations, inventory-based equations, and volume-based equations, in descending order. 74 4. CONCLUSIONS The first thesis objective was to investigate the relationships between total stand volume and aboveground component stand biomass (i.e. stem, foliage, and branch) using model-generated data. Predicted stand stem and branch biomass, using the TASS growth and yield model and existing biomass equations, increased with stand volume. Predicted stand foliage biomass increased in stands up to a threshold of volume/ha greater than 500 m3/ha, when foliage biomass either plateaus or has a slight decline. The second research objective was to show how the relationships between total stand volume and the aboveground biomass components change with stand characteristics (i.e. age, site index, and initial spacing). To consider such changes in the volume-biomass relationships, the relationships between biomass and age in relation to the other stand factors were examined first. For a given stand age, highly productive stands had more predicted biomass than less productive stands. Denser stands had more predicted biomass, particularly in young stands compared to mature stands. However, the difference in predicted biomass between an initially wide spaced and an initially close spaced stand diminished over time. This was especially evident in high quality sites. As far as biomass over volume trends and relationships were concerned, initial spacing matters. For a given predicted total stand volume, denser stands had less predicted stem and branch biomass except where stands had low predicted volumes on poor sites. On the other hand for the same volume, more foliage biomass;was predicted for the denser stands. A possible reason for this difference is that at a similar volume, the denser stands are younger than the more open stands of the same site quality. Younger tree's tend td have less stem and branch biomass 75 and more foliage biomass for a unit of stem volume. Given the same initial spacing, stands of varying site quality had similar predicted biomass over volume patterns, but differed when stands reached a certain biomass to volume ratio (i.e. high site quality stands reach similar biomass to volume ratios as those of low site quality stands, but at younger ages). The third research objective was to explore whether the ratios between component biomasses were affected by age, site quality, initial spacing, and stand volume. Over time, the proportion of foliage or branch biomass in total aboveground tree biomass was predicted to decrease then plateau, whereas the proportion in stem biomass was predicted to increase then plateau over time. With respect to site quality, highly productive stands are predicted to allocate more of their aboveground biomass to the boles and less to the foliage and branches. Given the same site quality and age, the biomass distributions using the Kurz (1989) and Gholz et al. (1979) equations differed for stands of the same initial spacing. The equations by Kurz (1989), predicted over time, showed proportionally more foliage and branch biomass in stands from closer spacing, but the reverse was shown using the Gholz etal. (1979) equations. Yet the same equations by the two authors showed in terms of a given stand volume, the same pattern: widely spaced trees tended to have proportionally more stem biomass and proportionally less foliage and branch biomass. Predicted biomass proportion ratios over volume differed with site productivity: less productive stands reached similar biomass proportion ratios as those in highly productive stands but at younger ages. The fourth objective was to investigate the first three objectives in the context of prediction equations. Generally, total stand volume was found to be a strong predictor of stand biomass components. However, young stands were often over-predicted by the regression 76 equations and the stand-level foliage biomass was the most difficult component to fit. Although the effects of initial spacing on biomass were found by examining the trends and relationships, in the regression analysis, initial spacing was not found to be a significant predictor variable. A possible explanation is that initial spacing is relatively poorly correlated with biomass over time since stand density changes greatly with time due to mortality. Nonetheless, stand density influences were presented by other variables that were found to be significant in biomass prediction. The number of trees per hectare was a relevant predictor variable in some regression equations and stand basal area was a significant predictor variable in all component volume to biomass regression functions. A l l component biomass regressions improved if stand variables other than stand volume were available. By comparing the predicted biomass proportion ratios generated by using tree-level equations to the ratios of predicted component biomass to predicted stem biomass derived from the developed regression equations, I found that the proportions were better predicted using, in descending order of preference, the all variables-based equations, the inventory-based equations, and the volume-based equations. The selection of a tree equation can affect estimates of stand-level biomass. Compared to tree equations based on one variable (e.g. dbh), tree equations that include significant predictor variables, other than dbh, can better estimate the variability found in biomass among trees. The accuracy in predicting tree-level biomass estimates may also affect the accuracy in the stand-level biomass estimates, since stand-level biomass is derived from the summation of all tree biomass in a stand. A l l relationships and equations reported in this study were based on model-simulated data. If actual stand biomass were measured from a variety of stands that differed in 77 site quality, initial spacing or density, genetics, and ages, there would be greater variability in the measured sample data compared to the simulated data. Therefore, the equations developed from a measured sample would likely not have as good of a fit (e.g. high coefficient of determination, or low standard error of the estimate), compared to the equations from the simulated data. The tree data from TASS represented a wider range than the sample data range used to develop the tree-level equations, with the exception of the Gholz et al. (1979) equation. Therefore, biomass comparisons should be made with caution outside these sampling tree ranges. The range of stand biomass for a given stand volume does vary with age, site quality, spacing, and selected tree-level equations. These stand characteristics should be considered in biomass research, and the tree-level equations chosen for stand biomass estimation is perhaps the most critical variable in the accuracy of biomass estimation. From a forest management perspective, bole biomass is the central component of total aboveground biomass, accounting for at least 80 percent in the 50 year-old or older simulated stands. Generally, there are fairly good estimates of bole biomass (as seen from most of the equations), but there are differences that are attributed to initial stand density and age. Greater uncertainty in all component biomass values is present in mature ( > 120 years old) and young ( < 20 years-old) stands. Because large trees are difficult to sample, research is limited in these mature stands. If the carbon stored from afforestation and reforestation may be claimed as sequestered carbon under the Kyoto Protocol, many potential emissions reduction buyers would be interested in high yield, short-rotation timber management. Therefore, it would be important to quantify biomass in young trees. If the management objectives were to maximize biomass and provide for high quality timber, dense planting on rich sites could be considered. Most forest 78 carbon studies predict aboveground carbon from the biomass to volume functions, and it can be seen in this study that this is a generalized function. Further improvements to this function can be made if the effects of stand age, site quality, and most importantly a measure of stand density (e.g. basal area/ha), are considered in addition to stand volume. 79 5. RECOMMENDATIONS From examining the trends and regression analyses, it was inferred that selected stand characteristics influence stand-level component biomass and component biomass proportions, but further research is recommended to verify the findings. For example, we could measure trees in undisturbed stands with different stand characteristics (e.g. site quality, stand density, age, and genetics) to find the range in biomass values, given a stand characteristic such as age. Sample plots could be established to measure tree and stand characteristics and tree biomass. The plot data could be used to estimate the stand-level biomass, which can then be compared for the different stand characteristics. The technique just described could also be used to explore spacing effects on biomass distribution over time, since conflicting results were found in my study; the relationships between the components ratios and stand characteristics are the least studied. 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Mono. 44: 233-252. 88 APPENDICES 89 APPENDIX 1: Summary of Additional Stand Statistics From TASS Variable N Missing N Mean Standard Deviation Minimum Maximum Merchantab le V o l u m e 3 (m 3 /ha) 837 63 793.25 553.92 1 2274 Mean Annua l Increment (12.5 c m diameter limit) (m 3 /ha) 837 63 6.83 3.88 0.03 17.37 Foliar Vo lume ( m 3 ) 900 0 10007.40 7556.35 3 42582 Foliar We igh t (t/ha) 900 0 15.39 4.28 0.60 20.64 Leaf A rea Index 900 0 11.57 3.22 0.45 15.52 Height to the Crown (m) 900 0 17.15 12.15 0.31 48.42 Crown Length (m) 900 0 8.01 4.48 0.28 19.28 Percent of Crown Length in Height (%) 900 0 28.52 13.69 7.8 65.46 Crown Wid th (m) 900 0 4.04 1.92 0.32 8.15 Crown Area (2D project ion on ground) ( m 2 ) 900 0 20.00 13.13 0.1 55.7 Average Total Vo lume (m 3 / t ree) 855 45 2.27 2.59 0.003 10.92 Average Merchantab le V o l u m e (m 3 / t ree) 843 57 2.24 2.53 0.023 10.727 Average Basal Area (m 2 / t ree) 829 71 0.17 0.15 0.01 0.62 Mean A g e (years) 900 0 103.22 57.78 8 199 a Merchantable volume is total volume not including the top 10 cm diameter inside bark, 30 cm stump and unmerchantable trees with diameter less than 12.5 cm. 90 APPENDIX 2: Summary of Tree-level Statistics in All Douglas-fir Stands Standard Variable N Missing N Mean Deviation Minimum Maximum Diameter at breast height (cm) 691973 104518 24.89 19.78 0.01 132.62 Height (m) 796386 105 17.81 14.29 0.01 83.23 Basal Area (m 2) 677094 119397 0.08 0.12 0.0001 1.3813 Total Volume (m 3 ) 663547 132944 1.05 2.02 0.001 27.798 Merchantable Volume 3 (m 3) 474550 321941 1.40 2.22 0.023 27.351 Total Age (years) 796491 0 71.56 56.68 3 200 X coordinate 796491 0 50.21 29.12 0.1 99.9 Y coordinate 796491 0 50.07 29.05 0.1 99.9 Height to the Crown (m) 796356 135 13.10 10.45 0.01 55.37 Crown Length (m) 555073 241418 6.75 5.81 0.01 45.53 Percent of Crown Length in Height (%) 555139 241352 39.13 17.35 0.54 82.4 Crown Area (2D projection on ground) (m 2) 555139 241352 14.87 17.18 0.04 137.6 Crown Width (m) 555139 241352 3.56 2.50 0.23 13.24 Foliar Volume (m 3) 522708 273783 12.55 16.73 0.01 191.27 Foliar Weight (kg/ha) 555139 241352 24.95 29.55 1.03 220.95 Projected Leaf Area (m 2) 555139 241352 187.54 222.10 7.75 1660.92 Bole Surface Area (m 2) 748941 47550 16.85 23.62 0.01 229.93 Branch Surface Area (m 2) 389248 407243 52.08 214.40 0 9020.06 a Merchantable volume is total volume not including the top 10 cm diameter inside bark, 30 cm stump and unmerchantable trees with diameter less than 12.5 cm. 91 Vi a CO o & oc E I "to* f to 3 CO to CO E o CQ c CO C o a E o O o b E E co CO 1 J g > co - * o I o E re £ o CO \-E a> co CO £Q CD - ~ CO co co ™ «> » <& CQ < E CD J= _ 0) C) r 10 E <o CD J= CO ~ -a E co c s— a> CM CM C (0 CC T-00 to I S - CD HL- ^ a. co (0 (0 CC O T3 C CO co LO 00 CNJ 00 co cc T3 c CO 0) ® CD u o CD CNI CD CM oo CD E S I => CO -5 6 co c CO cn co o —I cu oQ i -- .2 CD i -CD E CD 3 CO ^ 6 O [v. c co a> co o * . —I CD <=S >-1_ CD •= a o E CD 2 co X3 6 a> co cn c '—' co —: a> co o —I CD oQ i -- .2 CD i -•= a o CM E CD 3 CO ® co "* c •—' co O ) CO q —I Q) - .s> CD i -•= a o E CD 3 CO ^ 6 £ co h- Tt CT) I S -c ' ' co ^ o • — ' CD oS ,_ >_ CD CD - C o oo CNl cd oo CNJ CD CD cri CT> LO CO oo cri CD T t LO co LO CD CNJ CM LO CM CM CD cri co CD CM I CT> CNJ I CM co i oo CM CD X c CO _§ 'CD X CO I CD X c: co | CD X CT> CT> CO a> cri CM T t T t LO LO O CO CM 00 LO co CM I o o CD oo co CO I CD X CO CD CT> CD CT) c CO I 'CD X CN ON -* o CO I o LL CO E -55 co to « -Si M * CO co m 2 (0 co ^  co »=« m < E, CO E co 0) £ 4-* CO •= •§ E 1 CM LO CO co CNJ co c o E ^ CO £r co o> ^ ~"° iC o « cn CD = 4^  CO (0 (0 CO c y O) c •> 3 Q CD O C CO CO CD co CO oo oo co CNJ co CNJ o > O CNJ LO 2 o _l ~o c CO co 2 o _l T3 C CO o X i cO CU X ! 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S co co ro ro CO o 1— 1— 03 03 ro ro CO CO ro ro ro ro CO CO ro ro X) H D >» >s X> X i t- )H ro ro co cn ro ro x x X X co co ro o H O I i -8 .2 3 X co CO -a =5 c o P H X ; E 0 o o co co ro ro ro JQ j£> N N N "O "O x: x: — si 3 -"P r= 1_ L _ I _ co co co M M PH PH rrt CO CO N CO CO •2 T3 T 3 S -5 -5 co CJ o c c 3 xP T3 CQ _c > N T 3 3 ro b0 bX) 3 3 O O 3 Q PH M H W ON l> ON ON bO bJ3 3 3 O O Q Q SO 0 0 Os so c c ro CO CO c Br ro Br E 0 d 0 0 O X) _c H ro E CO •~-CO CO CO c HH CO ro E CO bO CO 0 1H pn| X "TO 0 E 3 c B ^ H ro HH c CO 00 CO CO c -a 0 3 CO P H E ncl qui 0 • 1—« 3 glan h ci ent c Cli glan CJ c CO c c 0 H i W ro UH D H ,"ro CQ E 0 H O c d 0 H .2 ch > N X "ro ro c ' c — CO ro 1— 1 a pla Aust egen CQ d lglas c c — 0 - H O c CO c o D H E o CJ o 3 03 kH c o ro 5 3 3 3 J2 " ^ E ^ CO c E c c c P. ro T 3 o * ^ -P X 13 ro in > S > N 3 3 H I -4—> C O C O S c* 3 S 03 ca 3 . o Q Q co m o t ON PH NO r- °o ON O H . f s i c ^ t f i n ^ ^ o o c 3 s O - H ( N i t c i t f i n » O h o o RT„„R-„„«^^RH(s)rs|(N|(N)0)0)CN|(N|(s) APPENDIX 4: Ratio of Foliage Biomass to Stem Biomass Over Time for A) Gholz et al. 1979 and B) Kurz 1989 B 60 cfl Cfl cn iom 50 OQ £ 40 £ o cn 30 eft to E o 20 in CD TO 10 to o LL o 0 o to DC L , , , , 1 , , , , 1 . - J , , 0 50 too Stand Age (years) 150 200 50 40 £ . 60 (fl (0 to E o CD E CD CO O Cfl cfl to E o in a> cn to O LL O 0 g ^—' to DC 304 20 10 ft-50 100 Stand Age (years) 150 200 SI 40, 5m Spacing SI 40, lm Spacing X SI 20, 5m Spacing SI 20, l m Spacing APPENDIX 5: Ratio of Branch Biomass to Stem Biomass Over Time for A) Gholz et al. 1979 and B) Kurz 1989 CO DC 50 100 150 Stand Age (years) 200 o to DC 50 100 150 Stand Age (years) 200 SI 40, 5m Spacing SI 40, lm Spacing X SI 20, 5m Spacing SI 20, l m Spacing 95 APPENDIX 6: Proportion of Foliage Biomass to Stem Biomass Over Total Volume for A) Gholz et al. 1979 and B) Kurz 1989 A B 0 500 1000 1500 2000 2500 o 0 500 1000 1500 2000 2500 e Total Volume (m3/ha) | Total Volume (m3/ha) • SI 40, 5m Spacing • SI 40, l m Spacing X SI 20, 5m Spacing A SI 20, lm Spacing APPENDIX 7: Proportion of Branch Biomass to Stem Biomass Over Total Volume for A) Gholz et al. 1979 and B) Kurz 1989 Total Volume (m3/ha) Total Volume (m3/ha) • SI 40, 5m Spacing • SI 40, lm Spacing X SI 20, 5m Spacing A SI 20, lm Spacing 96 

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