Improvement in accuracy of aboveground biomass estimation in Eucalyptus nitens plantations: Effect of bole sampling intensity and explanatory variables

1 Improvement in accuracy of aboveground biomass estimation in 1 Eucalyptus nitens plantations: effect of bole sampling intensity and 2 explanatory variables 3 César Pérez-Cruzado1,2,*, Roque Rodríguez-Soalleiro1,2 4 1 Sustainable Forest Management Unit, University of Santiago de Compostela, 5 2Crop Production Department, University of Santiago de Compostela, 6 E-27002 Lugo, Spain 7 * Corresponding author. Tel.: (+34) 982 285900 Ext 23108; fax: (+34) 982 285926 8 E-mail address: cesar.[email protected] 9 10 11 12 13 14 15 16 17 18 19 20 *Manuscript Click here to download Manuscript: Prez-Cruzado & Rodrguez-Soalleiro (2011).doc Click here to view linked References 2 Improvement in accuracy of aboveground biomass estimation in 1 Eucalyptus nitens plantations: effect of bole sampling intensity and 2 explanatory variables 3 César Pérez-Cruzado1,2,*, Roque Rodríguez-Soalleiro1,2 4 1Unit of Sustainable Forest Management, University of Santiago de Compostela, 5 2Crop Production Department, University of Santiago de Compostela, 6 E-27002 Lugo, Spain 7 * Corresponding author. Tel.: (+34) 982 285900 Ext 23108; fax: (+34) 982 285926 8 E-mail address: [email protected] 9 10 Abstract: 11 Two sets of aboveground biomass equations were fitted for stem only and stem plus 12 crown predictive variables in Eucalyptus nitens plantations in Northern Spain. A sample of 40 13 trees was chosen after a complete study of variation in tree height and diameter in the region. 14 The trees were felled and the biomass was divided into the following components: wood, 15 bark, thick branches, thin branches, twigs, leaves and dead branches along the stem. Bole 16 biomass was estimated by systematic subsampling of one 5 cm-thick disk every 0.5 m. Such 17 intensive subsampling enabled determination of the effect of subsampling intensity on 18 accuracy and bias of wood estimation, considering two ratio-type estimators: stem weight to 19 dry matter, determined by the complete weighing (CW) method (i.e. of the fresh weight of the 20 entire stem) and volume to dry matter, determined by the partial weighing (PW) method. The 21 changes in moisture content and basic density along the stem explained the serious risk of dry 22 mass or weight overestimation when a systematic subsample is considered. The average basic 23 density was usually found at a relative height of 30-35% along the stem. The default choice of 24 3 the bottom disk or log as the first section resulted in overestimations for the CW method and 1 underestimations for the PW one. The biomass equations were fitted by seemingly unrelated 2 regression, with corrections for heteroscedasticity carried out by weighted fitting. Diameter at 3 breast height was the best explanatory variable, and the inclusion of height did not improve 4 the accuracy, except for wood. The inclusion of crown variables improved the predictive 5 ability for crown fractions, increasing the accuracy for estimating thick branches (by 10.8%), 6 twigs (by 19.1%) and leaves (by 17.3%). The biomass of each fraction decreased in the 7 following order: wood>bark>thick branches>dead branches along the stem>leaves>thin 8 branches>twigs. The changes in these percentages with diameter class and the predictive 9 ability of the fitted equations were also studied. 10 Keywords: Eucalyptus nitens, biomass, ratio type estimators, wood basic density, wood 11 moisture; crown variables 12 13 1. Introduction 14 Destructive sampling and subsequent regression analysis is the most common method 15 used to estimate tree biomass (Parresol, 1999). Biomass estimation at tree level is a necessary 16 first stage in estimating stand biomass, and the main sources of error in this process are: i) 17 selection of trees for sampling; ii) measurement of independent and dependent variables in 18 sampling trees; iii) choice of a suitable form of the allometric relationship and values for any 19 adjustable parameters in the equation; iv) field measurement of the independent variables in 20 the objective population, and v) application of allometric equations to objective populations 21 for individual tree biomass estimation and summation to obtain stand estimates (Cunia, 1987, 22 Ketterings et al., 2001). Each of these steps has an associated error that must be minimized; 23 the errors involved in step ii are the least well studied (Satoo and Madgwick, 1982, Cunia, 24 1987, Parresol, 1999, Ketterings et al., 2001). 25 4 The errors in the assessment of sample tree dependent variables are strongly influenced 1 by the procedure (Cunia, 1987): i) subsampling selection, ii) fresh and dry weight estimation, 2 and iii) subsampling intensity. With small trees, fresh and dry weighing of the entire tree is 3 not time consuming nor expensive and is therefore recommended (Parresol, 2001). However, 4 direct measurement becomes more expensive as tree size increases, and subsampling becomes 5 inevitable (Satoo and Madgwick, 1982, Parresol, 1999). Fresh weight can be measured 6 directly or estimated by several methods. One of the most commonly used methods of 7 determining the fresh weight of trees and estimating the dry weight is to use ratio-type 8 estimators (Briggs et al., 1987), in which the relationships between dry/fresh weight or dry 9 weight/fresh volume are assessed in a sample and applied to the rest of the tree for dry weight 10 estimation. The main advantage of these methods is the simplicity of application and 11 determination, although it is well known that ratio estimators are biased (Cunia, 1979, 12 Valentine et al., 1984). 13 Some methods provide unbiased, efficient estimations, such as randomized-branch 14 sampling (RBS) and importance sampling (IS) methods, which use auxiliary information to 15 select elements in the sample to reduce the variance of the estimator (Valentine et al., 1984, 16 Parresol, 1999). RBS is a type of multi-stage probability sampling, which is used to select a 17 path so that resultant segments of the path comprise a probability sampling of the entire tree. 18 IS is a continuous analog involving sampling discrete units with probability proportional to 19 size (Gregoire et al., 1995). These methods are of interest for estimating fractions such as 20 branches or foliage, although in practice they are time-consuming and difficult to apply. 21 To apply ratio type estimators, stems can be weighed and disks removed to determine 22 moisture content (by the complete fresh weighing, CW method) or volume can be estimated 23 and short sample logs weighed to obtain volume to mass conversion factors (by the partial 24 weighing, PW method). Subsampling across the bole can be done by random stratified 25 5 sampling, as carried out by Briggs et al. (1987), although most researchers use a fixed number 1 of sections across the stem, with the position chosen systematically (i.e. (Saint-André et al., 2 2005)), randomly, or with a probability proportional to a given dimension. This was the case 3 for Kleinn and Pelz, (1987), who chose disks with a probability of selection proportional to 4 estimated volume. On the other hand, the PW method is preferred for large trees in sites with 5 difficult access, as fresh weighing of the whole stem is quite laborious and time consuming 6 (Snowdon et al., 2000). In the CW method, the distribution of moisture along the stem is the 7 main source of error for dry weight estimation, whereas in the PW method, it is the variation 8 in basic density along the bole height that affects that error. In both cases, sampling intensity 9 and distribution should guarantee a suitable description of the variability in moisture content 10 and specific density. 11 Diameter at breast height (d) and total height (h) are the most common dependent 12 variables used in biomass regression, because of their ease of measurement and predictive 13 capacity (Parresol, 1999, Snowdon et al., 2000). However, because of the current increasing 14 interest in obtaining accurate predictions of crown fractions for bioenergy, nutrient stability 15 and silvicultural or ecological studies, there is a corresponding increasing interest in crown 16 biomass modelling. Some authors have observed that the use of crown variables as 17 explanatory variables improves the accuracy of biomass equations (Satoo and Madgwick, 18 1982, António et al., 2007). In biomass studies in which high precision is required for crown 19 fractions, and destructive sampling cannot be applied, highly accurate models are required. 20 The objectives of the present study were: i) to obtain biomass estimation tools for a fast 21 growing species, Eucalyptus nitens, in northwestern Spain, considering the most complete set 22 of aboveground components; ii) to evaluate the bias and accuracy of wood biomass estimation 23 for different intensities of systematic subsampling across the stem and two ratio-type 24 estimators (dry/fresh weight and dry mass/fresh volume), iii) to evaluate the increased 25 6 accuracy derived from the inclusion of crown variables in the estimation of individual tree 1 biomass components, and iv) to evaluate the ability of the proposed equations to estimate the 2 proportion of each biomass component over total aboveground biomass, for a range of 3 diameter classes. 4 2. Materials and methods 5 2.1. Study site and trees sampled 6 This study was carried out in northwestern Spain, in an inland area located at elevations 7 of 500 to 1000m, with average precipitation of 900-1200 mm and average annual temperature 8 of 12-13ºC (Martínez Cortizas and Pérez Alberti, 1999). Although frost occurrence limits 9 planting of the most common Eucalyptus species in Spain (Eucalyptus globulus Labill.), 10 Eucalyptus nitens (Deane & Maiden) Maiden was successfully introduced in the mid 1990s, 11 providing yields of 15-50 m3 ha-1 yr-1 (Pérez-Cruzado, 2009). 12 As the aim of the present study was to construct biomass models that are as 13 representative as possible, sampling consisted of two phases: 1) study of the variability of the 14 most commonly used independent variables in biomass equations at tree level (d and h, see 15 below) across the distribution area, and 2) destructive sampling of trees covering the observed 16 range (Parresol, 1999). For this purpose, 76 plots were established (see location in Fig. 1), 17 covering the observed range of ages and site qualities, with a minimum plot size of 314 m2, 18 which is generally suitable for biomass estimation procedures in plantations (Satoo and 19 Madgwick, 1982). 20 A sample size of 40 trees was chosen because of the low variability in site conditions 21 and densities of plantations, most of which were established with the MacAlister provenance. 22 The sampled trees were chosen in two steps, two trees per diameter and height class were first 23 selected, and 16 additional trees were then chosen, considering the relative importance of each 24 diameter class in the population. The aim of this procedure was to cover the full range of tree 25 7 size, which is shown for height and diameter in Fig. 2. Trees were felled in 12 plots, in which 1 the values of the quadratic mean diameter and d of the trees sampled was similar; undamaged, 2 healthy trees that represented the dominant and codominant strata, were chosen. The average 3 standard deviation and range of representative stand and single tree variables, for both the 4 population and the sample are shown in Table 1. The variability in crown variables was 5 similar to that observed in stem variables, unlike in other studies (Satoo and Madgwick, 6 1982). 7 The following variables were measured in the sample trees while still standing: diameter 8 at breast height (d, cm) and stump diameter at 0.15 m (dst, cm), both measured in two 9 perpendicular directions to the nearest mm; total height (h, m) and live crown base height, 10 defined as the height of the first live branch insertion in the stem (hcb, m), both measured to 11 the nearest dm; crown diameter (dc, m) measured in two perpendicular directions following 12 the cardinal points to the nearest cm. Living crown length (hc, m) was estimated as difference 13 between total height (h) and live crown basis height (hcb, m). Crown volume (vc) was 14 calculated from hc and dc by assimilating the crown shape to an ellipsoid (1). Descriptive 15 statistics for these variables are shown in Table 2. 16             223 42 cc c hd v  (1) 17 2.2. Ratio type estimators and subsampling 18 The felled trees were cut into 0.5 m logs to a small-end diameter of 7 cm. The logs were 19 weighed fresh and a systematic subsample of one 5 cm-disk in the bottom part of each log 20 was taken, also considering a further disk at the top of the stem. Sample disks were weighed 21 fresh and transported to the laboratory in plastic bags. The over and under-bark diameters of 22 8 the disks were measured in two directions and the bark and wood were then separated and 1 weighed. 2 For each disk, the dry wood weight was measured after oven drying at 105ºC to constant 3 weight and the ratio of the dry/fresh weight of the wood was determined. Only one composite 4 sample per tree was considered for the bark. Fresh bark of all disks was weighed jointly, and 5 dried to determine dry bark weight, thus enabling the ratio of dry/fresh weight of bark to be 6 obtained for each tree. 7 The dry weight of wood and of bark in each log was calculated from the average ratios 8 calculated for the delimiting disks. The total wood (Ww, to a small-end diameter over bark of 9 7cm) and bark (Wb, evaluated till the threshold diameter considered for wood) dry biomass in 10 each tree was calculated as sum of the biomass of each log. 11 Four biomass fractions were considered for the crown: thick branches (WTb, diameters 12 over bark 2-7cm), which also include the tops of the boles, thin branches (Wtb, diameters over 13 bark 0.5-2cm), twigs (Wt, diameter less than 0.5 cm) and leaves (Wl). Dead branches in the 14 stem (Wdb) is also an important fraction in Eucalyptus nitens. Crown biomass was first 15 fractioned in the field into three groups: WTb, Wdb and the sum of Wtb, Wt and Wl, and then 16 weighed fresh, with a balance, to the nearest 10g. A subsample of 10-15% of fresh weight of 17 each fraction was taken to represent the top, medium and bottom part of the crown. These 18 subsamples were weighed in the field, with scales, to the nearest 0.01g. 19 The composite subsample of Wtb, Wt and Wl, was fractioned and weighed in the 20 laboratory and the proportion of each fraction was determined to enable estimation of the 21 fresh weight of each crown fraction. The dry weight of each fraction was then estimated from 22 the dry/fresh weight ratios. 23 2.3. Methodologies for bole mass estimation 24 9 The information obtained enabled comparison of two methods of estimating bole mass 1 or weight at a range of sampling intensities. The CW method consisted of determining the 2 complete stem weight and estimating dry weight from disks. Disk subsampling intensity was 3 modified considering a series of inter-disk distances which were multiples of 0.5. For each 4 inter-disk distance tested, there were several solutions, depending on the height of the first 5 section considered. For the logs between two disks, the dry weight estimation was calculated 6 from the average dry weight wood ratio of each disk, and for basal and terminal logs the disks 7 immediately above or below the log were considered. 8 For the PW method, it was considered that only one part of the stem was weighed, and 9 for the rest of the tree the volume was calculated from diameter under bark measured every 10 0.5 m along the stem and by use of the Smalian formula. The length of the weighed and cubed 11 log was made to range between 0.5m and the total stem height (up to a small-end diameter of 12 7cm), considering a variable position of the log along the stem. The fresh weight of the log 13 was transformed to dry weight by considering the moisture content derived from the whole set 14 of disks taken each 0.5 m. Volume to dry weight ratios were then used to estimate the total 15 dry mass of the stem by multiplying by the calculated volumes. 16 Both methods and sampling intensities were compared with the results obtained by the 17 CW method and disk equidistance of 0.5 m, considering the relative difference in the biomass 18 estimation for each tree (2). 19   100  W WW ˆ RD (2) where W ˆ is the predicted bole mass value with each sampling methodology and intensity. 20 The combinations of inter-disk distances, weighed log lengths and starting point along 21 the bole provided a relative difference value, and these were plotted against subsampling 22 intensity for different diameter classes. The 95% confidence intervals were obtained 23 16 3.3. Proportions of each biomass component 1 The statistics for the dry weight biomass fractions considered in the present study are 2 shown in Table 1. Wood is particularly important in the total biomass, representing about 3 70% of total dry weight for the average tree size, which emphasizes the importance of its 4 accurate estimation. The next fractions in importance are bark (10%) and thick branches, dry 5 branches, leaves, thin branches and twigs. The relative proportions of each component, 6 plotted against diameter, including a set of 8 small trees which were not used for fitting, are 7 shown in Fig. 11. The proportion of some of these components in trees of different diameter 8 class have been used as parameters in physiological growth models, and accurate estimation 9 by use of the models proposed in this paper is desirable. 10 The proportion of each component related to total aboveground biomass is becoming 11 critical in a scenario of increasing harvesting of biomass components that were previously left 12 in place in forest soils. The proportion of wood, commonly referred to as the harvest index, 13 increased with diameter (Fig. 11), although the trend was not continuous because of the need 14 to consider a threshold diameter. Consequently, the component of thick branches may account 15 for a large share of total aboveground biomass for trees with a diameter still too small to have 16 a significant wood fraction. The bark fraction was defined as the bark fraction in the stem, and 17 the bark of sections less than 7 cm in diameter was included in thick or thin branches, which 18 explains the low percentages shown for diameters less than 12 cm. As a result, the equations 19 presented here would provide reasonable estimates of biomass component percentages for 20 diameters larger than 12 cm. For smaller diameters, exclusive use of the equation predicting 21 total biomass is recommended. 22 4. Discussion 23 17 4.1. Stem biomass estimation 1 The results of this study show that the error may be important, and will depend on the 2 intensity of subsampling, when ratio-type estimators are used to estimate dry weight. The 3 error also depends on the method used (complete fresh weight or partial fresh weight) and on 4 the average tree size. Other authors have observed that ratio-type estimators provide biased 5 estimates (Cunia, 1979, Valentine et al., 1984, Briggs et al., 1987). These overestimates are as 6 large as the decreases in both subsampling intensity and average tree size. Overestimation is 7 clearly a more serious error than underestimation (Satoo and Madgwick, 1982) because it 8 does not err on the side of safety i.e. for carbon accounting procedures. 9 Wood moisture content and basic density change along the stem (Satoo and Madgwick, 10 1982) (Figs. 5 and 6), and affect the estimation of dry biomass by the CW and PW methods 11 respectively. Minimum moisture content and basic density occur in the basal part of the stem, 12 which is obviously where most of the accumulated weight and volume occur. This effect must 13 therefore be taken into account with a sufficient and well distributed number of subsamples 14 along the stem. One way of addressing this problem, when taper functions are available, is the 15 density integral approach (Parresol and Thomas, 1989). The weighed average is an alternative 16 method that gives more importance to those observations in the lower part of the stem, and 17 therefore more closely related to volume. 18 Chave et al. (2001) reported that the biomass values of the smallest trees strongly affect 19 the values of the model parameters in the allometric relation. This effect is even stronger 20 when a weighted adjustment methodology is used, because the smallest trees, which are less 21 variable, are more important than the largest trees because of heteroscedasticity correction. It 22 is therefore advisable to obtain the complete dry weight of the stem of small trees. 23 The degree of accuracy required depends on the objective of the estimation, although 24 equilibrium between sampling intensity and the level of precision must be ensured (Brown et 25 18 al., 1995). If ratio-type estimators are chosen for stem dry biomass estimation, a relatively 1 intensive subsampling scheme should be implemented, as others authors indicated for both 2 ratio-type and density-integral methods (Parresol, 1999). Comparing the methods considered 3 here, the CW method produced better results for the largest dimensional class than the PW 4 method (Figs. 3 and 4). This is because, for a given length of cubed and weighed part, the 5 proportion over total stem (as an indicator of sampling intensity) differs depending on tree 6 size, and therefore becomes less important as tree size increases. This must be taken into 7 account because the PW method is usually used for large trees in which complete weighing is 8 time-consuming. 9 The results clearly show the trends in relative errors derived from a default 10 consideration of the bottom disk or the bottom log as the first section to measure. It is 11 advisable, if systematic sampling is to be used, to establish the subsampling intensity before 12 randomizing the position along the stem of the first disk or log to be measured. In the case of 13 the PW method it is not recommended to take only one sample log per tree, although this was 14 the approach used in this study. The subsampling intensity should be split along the stem, and 15 a good representation of the bole area where average basic density is likely to be found is 16 advisable. Most published papers do not provide information about the proportion of weighed 17 and cubed logs or their distribution along the stem, although the most reasonable distribution 18 would be systematic or random, with the subsampling intensity chosen on the basis of 19 statistical criteria. 20 21 4.2. Biomass equations from stem and crown variables 22 Although it is known that d, h and W are closely related (Satoo and Madgwick, 1982), h 23 is not always included in biomass equations together with d because both are correlated and 24 inclusion of h adds only negligible accuracy (Jokela et al., 1986, Ter-Mikaelian and 25 19 Korzukhin, 1997, Johansson, 1999, Verwijst and Telenius, 1999, Snowdon et al., 2000, 1 Brown, 2002, Porté et al., 2002, Jenkins et al., 2003). In this study, inclusion of h together 2 with d only resulted in improved accuracy in the case of wood, although other authors have 3 reported significant improvement for several fractions (Loomis et al., 1966, Pearson et al., 4 1984, Bartelink, 1996, Reed and Tomé, 1998, Monserud and Marshall, 1999). In their study 5 on Eucalyptus globulus, António et al. (2007) observed improvements in the sum of residual 6 squares of 72%, 8%, 12% and 10% for wood, bark, leaves and branches respectively, after 7 inclusion of h together with d. It is possible that in the present study the tree sample was not 8 representative of the entire variability in height for a given diameter. 9 Some studies included h and d in biomass models, together with density, age and site 10 index (Ter-Mikaelian and Parker, 2000, António et al., 2007), and these models are therefore 11 suitable for comparing different sites (Ketterings et al., 2001). Other studies included age as 12 an independent variable in biomass equations (Porté et al., 2002, Saint-André et al., 2005), 13 thus producing dynamic models with which biomass increments can be estimated by 14 derivative analysis. Although individually dst worked well as a predictor, it is seldom 15 measured in forest inventories. On the other hand, it is sometimes useful to estimate dry 16 biomass when trees are already cut down and only stump dimensions are available. 17 It has been observed that some crown variables work well as predictors of crown 18 fractions (Clark, 1982, Satoo and Madgwick, 1982, Carvalho and Parresol, 2003). In the 19 present study, inclusion of crown variables improved the RMSE by 1.8%, 10.8%, 19.1% and 20 17.3% for respectively dead branches, thick branches, twigs and leaves, in the individual fit. 21 These improvements are smaller than those obtained by António et al. (2007) for Eucalyptus 22 globulus in Portugal, probably because of the lower genetic variability in the plantations 23 considered in that study. The best improvement was for leaves, which implies better 24 estimations of a fraction that is very difficult to predict and is very important as regards 25 20 nutrition and ecology. Overall, the results indicate a low accuracy of estimation of the bark 1 fraction in the present study, in comparison with reports for other species of Eucalyptus. 2 Wood, bark and thin branches depend on the same variables in both systems of equations, and 3 the results obtained by simultaneous fitting were generally only slightly less accurate. For 4 leaves, the reduction in R2Adj derived from simultaneous fitting was 6.3%. 5 The ability of the fitted biomass equations to evaluate the proportion of each 6 aboveground biomass component for a range of diameters has seldom been studied. The 7 proportions are often considered as parameters for ecophysiological models, particularly for 8 small diameters (Sands and Landsberg, 2002). The present results show that, if a threshold 9 diameter is considered for defining a wood component, minimum breast height diameter must 10 be considered to define the range of use of the biomass components equations, if sound 11 estimation of these percentages is sought. 12 5. Conclusions 13 Two systems of equations were fitted for aboveground biomass components of 14 Eucalyptus nitens. The inclusion of crown variables as predictive variables provided poorer 15 results for total biomass, wood and thin branches, but improved the accuracy of estimation for 16 twigs, leaves, thick branches and dead branches. 17 Stem subsampling affects estimation of the wood fraction. If a systematic subsample of 18 disks or logs is taken, the variation in moisture content or basic density along the stem should 19 be considered. Less intensive sampling usually leads to overestimation of biomass with both 20 methods (complete fresh weighing or partial fresh weighing). The minimum subsampling 21 intensity for an assumed ±5% RD in wood dry biomass estimation depends on the tree 22 diameter class, with a range of 0.75 to 0.95 disks m-1 in the CW method. Use of the PW 23 method would require very intense subsampling to reduce the relative error, independently of 24 21 tree size. The average basic density usually occurs at a relative height of 30-35% along the 1 stem. It is not always advisable to choose the first section of study at the bottom of the stem. 2 Acknowledgements 3 The authors thank Elena Fernández-Rivas, Fernando Pérez-Rodríguez and Juan Gabriel 4 Alvarez for assisting with fieldwork and data analysis. The study was funded by the Spanish 5 Ministry of Education and Science (SUM2006-00006-00-00) and a FPU-MEC Spanish 6 Fellowship awarded to the correspondent author. 7 References 8 Álvarez-González, J.G., Rodríguez-Soalleiro, R., Rojo-Alboreca, A., Resolución de 9 problemas del ajuste simultáneo de sistemas de ecuaciones: heterocedasticidad y 10 variables dependientes con distinto número de observaciones, 2007. Cuadernos SECF. 11 23: 35-42. 12 António, N., Tomé, M., Tomé, J., Soares, P., Fontes, L., 2007. Effect of tree, stand, and site 13 variables on the allometry of Eucalyptus globulus tree biomass. Can. Jour. For. Res. 37, 14 895-906. 15 Bartelink, H.H., 1996. Allometric relationships on biomass and needle area of Douglas-fir. 16 For. Ecol. Manage. 86, 193-203. 17 Breusch, T.S., Pagan, A.R., 1979. A simple test for heteroscedasticity and random coefficient 18 variation. Econometrica. 47, 1287-1294. 19 Briggs, R.D., Cunia, T., White, E.H., Yawney, H.W., 1987. Estimating sample tree biomass 20 by subsampling: some empirical results. Estimating Tree Biomass Regressions and 21 Their Error.Proceedings of the Workshop on Tree Biomass Regression Functions and 22 their Contribution to the Error of Forest Inventory Estimates.Compiled by EH Wharton 23 and T.Cunia.USDA For.Serv.Gen.Tech.Rep.NE-117 119-127. 24 Broad, L.R., 1998. Allometry and Growth. For. Sci. 44, 458-464. 25 Brown, I.F., Martinelli, L.A., Thomas, W.W., Moreira, M.Z., Ferreira, C.A.C., Victoria, R.A., 26 1995. Uncertainty in the biomass of Amazonian forests: an example from Rondônia, 27 Brazil. For. Ecol. Manage. 75, 175-189. 28 Brown, S., 2002. Measuring carbon in forests: current status and future challenges. 29 Environmental Pollution 116, 363-372. 30 Carvalho, J.P., Parresol, B.R., 2003. Additivity in tree biomass components of Pyrenean oak 31 (Quercus pyrenaica Willd.). For. Ecol. Manage. 179, 269-276. 32 Chave, J., Riéra, B., Dubois, M.A., 2001. Estimation of biomass in a neotropical forest of 33 French Guiana: spatial and temporal variability. J. Trop. Ecol. 17, 79-96. 34 Clark, A., Predicting biomass production in the South, 1982. Hotverdt, J.E., Jackson B.D:, 35 (Eds.), In: Predicting Growth and Yield in the Mid-South. 31st Annual Forest 36 Symposium, 119-139. 37 Clutter, J.L., Fortson, J.C., Pienaar, L.V., Brister, H.G., Bailey, R.L., 1983. Timber 38 Management: A Quantitative Approach. John Wiley and Sons, New York. 39 Cunia, T., 1979. On sampling trees for biomass tables construction: Some statistical 40 comments. In: Frayer, W.E., (Ed.).Forest resource inventories, Vol. 2. Colorado State 41 University, Fort Collins, Colorado, pp. 643-664. 42 22 Cunia, T., Construction of tree biomass tables by linear regression techniques, 1987. Wharton, 1 E.H., Cunia, T., (Eds.), In: Estimating Tree Biomass Regressions and their Error: 2 Proceedings of the Workshop on Tree Biomass Regression Funktions and their 3 Contribution to the Error of Forest Inventory Estimates. USDA Forest Service, 27-36. 4 Gregoire, T.G., Valentine, H.T., Furnival, G.M., 1995. Sampling methods to estimate foliage 5 and other characteristics of individual trees. Ecology. 76, 1181-1194. 6 Harvey, A.C., 1976. Estimating Regression Models with Multiplicative Heteroscedasticity. 7 Econometrica. 44, 461-465. 8 Jenkins, J.C., Chojnacky, D.C., Heath, L.S., Birdsey, R.A., 2003. National-Scale Biomass 9 Estimators for United States Tree Species. For. Sci. 49, 13-35. 10 Johansson, T., 1999. Biomass equations for determining fractions of pendula and pubescent 11 birches growing on abandoned farmland and some practical implications. Biomass & 12 Bioenergy. 16, 223-238. 13 Jokela, E.J., Van Grup, K.P., Briggs, R.D., White, E.H., 1986. Biomass estimation equations 14 for norway spruce in New York. Can. Jour. For. Res. 16, 413-415. 15 Ketterings, Q.M., Coe, R., van Noordwijk, M., Ambagau, Y., Palm, C.A., 2001. Reducing 16 uncertainty in the use of allometric biomass equations for predicting above-ground tree 17 biomass in mixed secondary forests. For. Ecol. Manage. 146, 199-209. 18 Kleinn, C., Pelz, D.R., 1987. Subsampling trees for biomass. In: Wharton, E.H., Cunia, T., 19 (Eds.).Estimating Tree Biomass Regressions and their Error: Proceedings of the 20 Workshop on tree Biomass Regression Functions and their Contribution to the Error of 21 Forest Inventory Estimates. USDA Forest Service, Broomall, PA: U.S., pp. 225-227. 22 Loomis, R.M., Phares, R.E., Crosby, J.S., 1966. Estimating foliage and branchwood quantities 23 in shortleaf pine. For. Sci. 12, 30-39. 24 Martínez Cortizas, A., Pérez Alberti, A., 1999. Atlas Climático De Galicia. Xunta de Galicia, 25 Santiago de Compostela. 26 Monserud, R.A., Marshall, J.D., 1999. Allometric crown relations in three northern Idaho 27 conifer species. Can. Jour. For. Res. 29, 521-535. 28 Neter, J., Wasserman, W., Kutner, M.H., William Wasserman, M.H.K., 1989. Applied Linear 29 Regression Models. Irwin Homewood, Ill, New York. 30 Parresol, B.R., 1993. Modeling multiplicative error variance: an example predicting tree 31 diameter from stump dimensions in baldcypress. For. Sci. 39, 670-679. 32 Parresol, B.R., 1999. Assessing Tree and Stand Biomass: A Review with Examples and 33 Critical Comparisons. For. Sci. 45, 573-593. 34 Parresol, B.R., 2001. Additivity of nonlinear biomass equations. Can. J. For. Res. 31, 865-35 878. 36 Parresol, B.R., Thomas, C.E., 1989. A density-integral approach to estimating stem biomass. 37 For. Ecol. Manage. 26, 285-297. 38 Pearson, J.A., Fahey, T.J., Knight, D.H., 1984. Biomass and leaf area in contrasting lodgepole 39 pine forests. Can. J. For. Res. 14, 259-265. 40 Pérez-Cruzado, C., 2009. Herramientas de gestión para plantaciones de Eucalyptus nitens 41 (Deane & Maiden) Maiden con el objetivo de fijación de carbono. University of 42 Santiago de Compostela. 43 Porté, A., Trichet, P., Bert, D., Loustau, D., 2002. Allometric relationships for branch and tree 44 woody biomass of Maritime pine (Pinus pinaster Ait.). For. Ecol. Manage. 158, 71-83. 45 Reed, D., Tomé, M., 1998. Total aboveground biomass and net dry matter accumulation by 46 plant component in young Eucalyptus globulus in response to irrigation. For. Ecol. 47 Manage. 103, 21-32. 48 Saint-André, L., M'Bou, A.T., Mabiala, A., Mouvondy, W., Jourdan, C., Roupsard, O., 49 Deleporte, P., Hamel, O., Nouvellon, Y., 2005. Age-related equations for above-and 50 23 below-ground biomass of a Eucalyptus hybrid in Congo. For. Ecol. Manage. 205, 199-1 214. 2 Sands, P.J., Landsberg, J.J., 2002. Parameterisation of 3-PG for plantation grown Eucalyptus 3 globulus. For. Ecol. Manage. 163, 273-292. 4 SAS Institute Inc, 2004. SAS/STAT 9.1 User's Guide. Cary, N.C. 5 Satoo, T., Madgwick, H.A.I., 1982. Forest Biomass. 152. 6 Schaegel, B.E., 1982. Boxelder (Acer Negundo L.) Biomass Component Regression Analysis 7 for the Mississippi Delta. For. Sci. 20, 617-628. 8 Snowdon, P., Eamus, D., Gibbons, P., Khanna, P.K., Keith, H., Raison, R.J., Kirschbaum, 9 M.U.F., 2000. Synthesis of Allometrics, Review of Root Biomass and Design of Future 10 Woody Biomass Sampling Strategies. Australian Greenhouse Office, Canberra. 11 Ter-Mikaelian, M.T., Korzukhin, M.D., 1997. Biomass equations for sixty-five North 12 American tree species. For. Ecol. Manage. 97, 1-24. 13 Ter-Mikaelian, M.T., Parker, W.C., 2000. Estimating biomass of white spruce seedlings with 14 vertical photo imagery. New Forests. 20, 145-162. 15 Valentine, H.T., Tritton, L.M., Furnival, G.M., 1984. Subsampling trees for biomass, volume, 16 or mineral content. For. Sci. 30, 673-681. 17 Verwijst, T., Telenius, B., 1999. Biomass estimation procedures in short rotation forestry. 18 For. Ecol. Manage. 121, 137-146. 19 White, H., 1980. A heterocedasticity-consistent covariance matrix estimator and a direct test 20 for heterocedasticity. Econometrica. 48, 817-838. 21 Zianis, D., Mencuccini, M., 2004. On simplifying allometric analyses of forest biomass. For. 22 Ecol. Manage. 187, 311-332. 23 24 25 24 TABLES 1 2 Table 1. Statistics for stand and single tree variables in the population (76 plots, 3864 trees) 3 and the sample plots (12 plots, 40 trees). 4 Stand variables Individual tree variables SI (m) N (stems ha-1) Age (yr) d (cm) h (m) All plots Average (Std. dev.) 15.3 (4.4) 1089 (280) 9.5 (4.2) 18.5 (7.5) 20.2 (6.4) Range 8.8 - 20.8 446 - 1560 2 - 18 1.0 - 59.6 2.2 - 48.3 Sample plots Average (Std. dev.) 15.7 (2.7) 1101 (223) 10.2 (2.8) 19.5 (7.7) 19.3 (5.5) Range 9.8 - 18.9 446 - 1401 2 - 13 1.1 - 47.0 2.4 - 35.1 Where SI is the site index (m at reference age of 6 years); N is stand density (stems ha-1), d is 5 diameter at breast height (cm), and h is the total height (m). 6 7 Table 2. Descriptive statistics of sampled trees. 8 Variable Average Maximum Minimum St. Dev. Independent variables d (cm) 20.84 41.55 3.95 10.04 dst (cm) 25.63 52.40 6.60 12.13 h (m) 19.94 30.80 4.40 7.27 hcb (m) 12.55 20.60 2.80 4.68 hc (m) 7.39 19.80 1.20 4.21 dc (cm) 3.50 8.55 1.25 1.66 vc (m3) 81.78 566.5 1.00 129.3 Dependent variables (kg tree-1) Wl 10.73 48.85 0.28 12.94 Wt 4.15 23.33 0.18 5.10 Wtb 4.40 18.46 0.04 4.53 WTb 13.57 75.65 1.29 18.71 Ww 168.43 599.5 0 176.9 Wb 24.59 111.3 0 28.33 Wdb 11.29 68.28 0.03 13.64 Wtot 237.2 838.2 2.54 248.1 Definitions of independent and dependent variables are given in sections 2.1 and 2.2, 9 respectively. Wtot refers to total aboveground biomass. 10 11 Table 3. Models selected for simultaneous fitting of each equation system. 12 Stem equation system Crown equation system Fraction Model RMSE MRES R2 Adj Model RMSE MRES R2 Adj Wtot  itot WW 37.9 2.86 0.98  itot WW 39.9 1.36 0.97 Wdb 1,2 b 1,1·db 10.6 0.32 0.40 2.3 2.2 b cb b 2.1 ·h·db 10.4 -0.04 0.42 Wb 1.4 b 1.3·db 15.3 0.72 0.71 2.5 b 2.4·db 15.3 0.30 0.71 Ww 1.71.6 bb 1.5 ·h·db 17.9 0.32 0.99 2.82.7 bb 2.6 ·h·db 18.2 -0.16 0.99 WTb 1.9 b 1.8·db 6.0 1.05 0.90 2.11 2.10 b c b 2.9 ·d·db 5.4 0.62 0.92 Wtb 1.11 b 1.10·db 2.2 0.13 0.76 2.13 b 2.12·db 2.4 0.24 0.71 Wt 1.13 b 1.12·db 2.1 0.07 0.83 2.16 2.15 b c b 2.14 ·d·db 1.7 0.26 0.89 Wl 1.15 b 1.14·db 5.6 0.25 0.81 2.19 2.18 b c b 2.17 ·h·db 4.6 0.15 0.87 25 Definitions of the different fractions are given in section 2.2. Wtot refers to total aboveground 1 biomass. 2 3 4 Table 4. Parameters for simultaneous fitting of equations. 5 Parameter Estimate Appr.SE Pr > |t| Parameter Estimate Appr.SE Pr > |t| b1,1 0.145 0.05 0.0063 b2,1 0.0079 0.0077 0.3137 b1,2 1.403 0.12 <.0001 b2,2 1.279 0.313 0.0003 b1,3 0.013 0.0083 0.1177 b2,3 1.254 0.411 0.0044 b1,4 2.361 0.1892 <.0001 b2,4 0.0318 0.016 0.0545 b1,5 0.0094 0.0024 0.0004 b2,5 2.1079 0.156 <.0001 b1,6 2.0329 0.082 <.0001 b2,6 0.0149 0.0034 0.0001 b1,7 1.0562 0.1335 <.0001 b2,7 2.0515 0.081 <.0001 b1,8 0.000059 0.000064 0.3586 b2,8 0.8946 0.128 <.0001 b1,9 3.7599 0.2983 <.0001 b2,9 0.00082 0.0010 0.4124 b1,10 0.0128 0.005 0.0153 b2,10 2.6444 0.4403 <.0001 b1,11 1.8579 0.131 <.0001 b2,11 0.7627 0.265 0.0069 b1,12 0.00092 0.00049 0.07 b2,12 0.030047 0.0098 0.0042 b1,13 2.6322 0.159 <.0001 b2,13 1.590388 0.1168 <.0001 b1,14 0.0053 0.0034 0.1281 b2,14 0.006228 0.0028 0.0329 b1,15 2.3931 0.197 <.0001 b2,15 1.949093 0.1932 <.0001 b2,16 0.218899 0.01909 0.0259 b2,17 0.016847 0.0102 0.109 b2,18 1.515742 0.2651 <.0001 b2,19 0.774688 0.1934 0.0003 6 7 8 9 FIGURE CAPTIONS 10 11 Fig. 1. Location of the measured plots (dots) and the distribution of Eucalyptus nitens in 12 north-western Spain (shaded area). 13 14 Fig. 2. Height-diameter distribution of Eucalyptus nitens in an initial inventory in north-15 western Spain. 16 17 Fig. 3. Relative difference for three dimensional classes: DC1 (d<14cm; n = 6922), DC2 18 (14<d<24cm; n = 17075) and DC3 (d>24cm; n = 18360), plotted against sampling intensity 19 (disks per stem meter) for the CW method. Continuous black line: average value for all data; 20 dotted black lines: 95% confidence intervals for all data; continuous grey line: average value 21 for alternatives that include bottom log. n is the number of simulated alternatives for each 22 dimensional class. 23 24 Fig. 4. Relative difference for two dimensional classes: DC2 (14<d<24cm; n = 7712) and 25 DC3 (d>24cm; n = 12001), plotted against sampling intensity (fraction of stem height 26 weighed) for the PW method. Continuous black line: average value for all data; dotted black 27 lines: 95% confidence intervals for all data; continuous grey line: average value for 28 alternatives that include bottom log. n is the number of simulated alternatives for each 29 dimensional class. 30 31 6 Wtot y = 1,0202x - 3,6567 R2 = 0,9804 0 200 400 600 800 1000 0200 400 600 800 1000 Predicted Observed Ww y = 1,0057x - 0,7481 R2 = 0,9894 0 100 200 300 400 500 600 700 0100 200 300 400 500 600 700 Predicted Observed Wb y = 0,9851x + 0,4452 R2 = 0,7088 0 20 40 60 80 100 120 020 40 60 80 100 120 Predicted Observed Wdb y = 0,918x + 0,8766 R2 = 0,4261 0 10 20 30 40 010 20 30 40 Predicted Observed WTb y = 1,0166x + 0,4047 R2 = 0,916 0 20 40 60 80 020 40 60 80 Predicted Observed Wtb y = 1,0061x - 0,0508 R2 = 0,7756 0 5 10 15 20 0 5 10 15 20 Predicted Observed Wt y = 1,0723x - 0,2395 R2 = 0,9048 0 5 10 15 20 25 0 5 10 15 20 25 Predicted Observed Wl y = 1,0407x - 0,3666 R2 = 0,8821 0 10 20 30 40 50 010 20 30 40 50 Predicted Observed Fig. 10. Relationship between observed-predicted dry weight values for each biomass 1 component (kg tree-1) in the Crown system of equations. 2 3 4 7 0 10 20 30 40 50 60 70 80 90 010 20 30 40 d (cm) Proportion of aboveground biomass (%) Ww WTb Pred. Ww Pred, WTb 0 2 4 6 8 10 12 14 16 010 20 30 40 d (cm) Proportion of aboveground biomass (%) Wdb Wtb Pred. Wdb Pred. Wtb 0 5 10 15 20 25 010 20 30 40 d (cm) Proportion of aboveground biomass (%) Wb Pred. Wb 0 5 10 15 20 25 30 35 40 45 010 20 30 40 d (cm) Proportion of aboveground biomass (%) Wl Wt Pred. Wl Pred. Wt Fig. 11. Proportion of each biomass fraction over total aboveground biomass. Open figures: 1 trees used in developing biomass equations; filled figures: additional small trees; lines: 2 prediction of biomass equations. 3 4 5 6