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Background: Biomass regression equations are claimed to yield the most accurate biomass estimates than biomass expansion factors (BEFs). Yet, national and regional biomass estimates are generally calculated based on BEFs, especially when using national forest inventory data. Comparison of regression equations based and BEF-based biomass estimates are scarce. Thus, this study was intended to compare these two commonly used methods for estimating tree and forest biomass with regard to errors and biases. Methods: The data were collected in 2012 and 2014. In 2012, a two-phase sampling design was used to fit tree component biomass regression models and determine tree BEFs. In 2014, additional trees were felled outside sampling plots to estimate the biases associated with regression equation based and BEF-based biomass estimates; those estimates were then compared in terms of the following sources of error: plot selection and variability, biomass model, model parameter estimates, and residual variability around model prediction. Results: The regression equation based below-, aboveground and whole tree biomass stocks were, approximately, 7.7, 8.5 and 8.3%larger than theBEF-based ones. Forthe wholetreebiomass stock, the percentage of the total error attributed to first phase (random plot selection and variability) was 90 and 88 % for regression- and BEF-based estimates, respectively, being the remaining attributed to biomass models (regression and BEF models, respectively). The percent bias of regression equation based and BEF-based biomass estimates for the whole tree biomass stock were −2.7 and 5.4 %, respectively. The errors due to model parameter estimates, those due to residual variability around model prediction, and the percentage of the total error attributed to biomass model were larger for BEF models (than for regression models), except for stem and stem wood components. Conclusions: The regression equation based biomass stocks were found to be slightly larger, associated with relatively smaller errors and least biased than the BEF-based ones. For stem and stem wood, the percentages of their total errors (as total variance) attributed to BEF model were considerably smaller than those attributed to biomass regression equations. Keywords: Androstachys johnsonii Prain, Mecrusse, Root growth, Biomass additivity, Double sampling, Forest biomass inventory, Carbon allocation Background 1999; Brown 2002; IPCC 2006; Pearson et al. 2007): live Carbon dioxide sequestration and storage associated with aboveground biomass (AGB) (trees and non-tree vegeta- forest ecosystem is an important mechanism for regulat- tion), belowground biomass (BGB), dead organic matter ing anthropogenic emissions of this gas and contribute to (dead wood and litter biomasses), and soil organic matter. the mitigation of global warming (Husch et al. 2003). The Biomass can be measured or estimated by in situ sam- estimation of carbon stock in forest ecosystems must in- pling or remote sensing (Lu 2006; Ravindranath 2008; clude measurements in the following carbon pools (Brown GTOS 2009; Vashum and Jayakumar 2012). The in situ sampling, in turn, is divided into destructive direct bio- mass measurement and non-destructive biomass estima- Correspondence: tarqmag@yahoo.com.br Departamento de Engenharia Florestal, Universidade Eduardo Mondlane, tion (GTOS 2009; Vashum and Jayakumar 2012). Campus Universitário, Edifício no.1, 257, Maputo, Mozambique © 2015 Magalhães. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Magalhães Forest Ecosystems (2015) 2:28 Page 2 of 12 Non-destructive biomass estimation does not require type where the main species, many times the only one, harvesting trees; it uses biomass equations to estimate in the upper canopy is Androstachys johnsonii Prain biomass at the tree-level and sampling weights to estimate (Mantilla and Timane 2005). A. johnsonii is an evergreen biomass at the forest level (Pearson et al. 2007; GTOS tree species (Molotja et al. 2011), the sole member of the 2009; Soares and Tomé 2012). When biomass equations genus Androstachys in the Euphorbiaceae family. Mecrusse are fitted using least squares they are called biomass re- woodlands are mainly found in the southmost part of gression equations. Biomass regression equations are de- Mozambique, in Inhambane and Gaza provinces, and in veloped as linear or non-linear functions of one or more Massangena, Chicualacuala, Mabalane, Chigubo, Guijá, tree-level dimensions. On other hand, when they are fitted Mabote, Funhalouro, Panda, Mandlakaze, and Chibuto in such a way that specify tree component biomass as dir- districts. The easternmost Mecrusse forest patches, lo- ectly proportional to stem volume, the ratios of propor- cated in Mabote, Funhalouro, Panda, Mandlakaze, and tionality are then called component biomass expansion Chibuto districts, were defined as the study area and factors (BEFs). However, biomass equation (either regres- encompassed 4,502,828 ha (Dinageca 1997), of which sions or BEFs) are developed from destructively sampled 226,013 ha (5 %) were Mecrusse woodlands. Maps show- trees (Carvalho and Parresol 2003; Carvalho 2003; Dutca ing the area of natural occurrence of mecrusse in Inhnam- et al. 2010; Marková and Pokorný 2011; Sanquetta et al. bane and Gaza provinces and the study area, along with 2011; Mate et al. 2014; Magalhães and Seifert 2015 a, b, c). detailed description of the species and the forest type Biomass regression equations yield the most accurate can be found in Magalhães and Seifert (2015c) and estimates (IPCC 2003; Jalkanen et al. 2005; Zianis et al. Magalhães (2015). 2005; António et al. 2007; Soares and Tomé 2012) as long as they are derived from a large enough number of trees (Husch et al. 2003; GTOS 2009). Nonetheless, na- Data collection tional and regional biomass estimates are generally cal- The data were collected in 2012 and 2014. In 2012, a culated based on BEFs (Magalhães and Seifert 2015c), two-phase sampling design was used to determine tree especially when using national forest inventory data component biomass. In the first phase, diameter at breast (Schroeder et al. 1997; Tobin and Nieuwenhuis 2007). height (DBH) and total tree height of 3574 trees were Jalkanen et al. (2005) compared regression equations measured in 23 randomly located circular plots (20-m ra- based and BEF-based biomass estimates for pine-, spruce- dius). Only trees with DBH ≥5 cm were considered. In the and birch-dominated forests and mixed forests and con- second phase, 93 A. johnsonii trees (DBH range: 5–32 cm; cluded that BEF-based biomass estimates were lower and height range: 5.69–16 m) were randomly selected from associated with larger error than regression equations based those analysed during the first phase for destructive meas- biomass estimates. However, no similar studies have been urement of tree component biomass along with the vari- conducted for tropical natural forests. ables from the first phase. Maps showing the distribution The objective of this particular study was to compare of the 23 randon plots in the study area and in the differ- regression equations based and BEF-based above- and be- ent site classes are shown by Magalhães and Seifet (2015c) lowground biomass estimates for an evergreen forest in and Magalhães (2015). Mozambique with regard to the following sources of er- In 2014, additional 37 trees (DBH range: 5.5–32 cm; rors: (1) random plot selection and variability, (2) biomass height range: 7.3–15.74 m) were felled outside sampling model, (3) model parameter estimates, and (4) residual plots, 21 inside and 16 outside the study area. The 93 variability around model prediction. Therefore, the preci- trees collected in 2012 were used to fit tree component sion and bias associated with those estimates were crit- biomass regression models and determine tree compo- ically analysed. This study is a follow up of the study by nent BEFs, and those collected in 2014 (37 trees) were Magalhães and Seifert (2015b). However, unlike the study used to estimate the biases associated with regression by those authors, that considered only five tree compo- equation based and BEF-based tree component biomass nents, the current study is extended to 11 components estimates. (taproot, lateral roots, root system,stemwood,stembark, The felled trees (both from 2012 to 2014) were di- stem, branches, foliage, crown, shoot system, and whole vided into the following components: (1) taproot + tree), and to bias analyses not considered by Magalhães and stump; (2) lateral roots; (3) root system (1 + 2); (4) stem Seifert (2015b, c) for either method of estimating biomass. wood; (5) stem bark; (6) stem (4 + 5); (7) branches; (8) foliage; (9) crown (7 + 8); (10) shoot system (6 + 9); and Methods (11) whole tree (3 + 10). Tree components were sam- Study area pled and the dry weights estimated as desbrided by The study was conducted in Mozambique, in an ever- Magalhães and Seifert (2015, a, b, c, d, e) and Magalhães green forest type named Mecrusse. Mecrusse is a forest (2015). Magalhães Forest Ecosystems (2015) 2:28 Page 3 of 12 Data processing and analysis the selected weight function may not have been the best Tree component biomass one among all possible weights, it was the best approxi- The distinction between biomass regression equations (or mation found. simply regression equations) and biomass expansion fac- Linear models were preferred over nonlinear models tors (BEFs) may be confusing as BEF is a biomass equation because the procedure of enforcing additivity by using (equation that yields biomass estimates), it is a regression the same regressors is only applicable for linear models through the origin of biomass on stem volume where, (Parresol 1999; Goicoa et al. 2011) and because the pro- therefore, the BEF value is the slope. For clarity, in this cedure of combining the error of the first and second study, biomass regression equations refer to the biomass sampling phases in double sampling (Cunia 1986a) is lim- equations where the regression coefficients are obtained ited to biomass regressions estimated by linear weighted using least squares (Montgomery and Peck 1982) such least squares (Cunia 1986a). that the sum of squares of the difference between the ob- The regression equation based and the BEF-based bio- th th served and expected value is minimum (Jayaraman 2000), mass of the c component of the k tree in the h plot unlike BEF which is not obtained using least squares. (Ŷ ) is determined by Eq. (1) and Eq. (2), respectively: hk Biomass estimation typically requires estimation of tree Y ¼ b þ b D H ð1Þ hk 0 1 hk hk components and total tree biomass (Seifert and Seifert 2014). To ensure the additivity of minor component bio- Y ¼ BEF v hk c hk mass estimates into major components and whole tree ¼ BEF D H ff ð2Þ c hk hk biomass estimates, minor component, major component and whole tree biomass models were fitted using the same where v ,D and H represent stem volume, DBH and hk hk hk regressors (Parresol 1999; Goicoa et al. 2011). For this, th th tree height of the k tree in the h plot, ff and BEF rep- first the best tree component and whole tree biomass resent the average Hohenadl form factor (0.4460) and tree regression equations were selected by running various component BEFs of A. johnsonii estimated by Magalhães possible linear regressions on combinations of the inde- and Seifert (2015c). pendent variables (DBH, tree height) and evaluating Computing BEF-based biomass is similar to compute them using the following goodness of fit statistics: coef- the biomass with a regression equation of tree compon- ficient of determination (R ), standard deviation of re- tent biomass on stem volume passing through the origin, siduals (S ), mean residual (MR), and graphical analysis y.x where, therefore, b = 0 and b = BEF . In fact, in ratio 0 1 c of residuals. The mean residual and the standard deviation estimators, the ratio R (BEF value, in this case) is the re- of residuals were expressed as relative values, hereafter re- gression slope when the regression line passes through ferred to as percent mean residual (MR (%)) and coeffi- the origin (Johnson 2000). Given that fact, Eqs. (1, 2) cient of variation of residuals (CV (%)), respectively, can be presented as one, in matrix form as follows: which are more revealing. The computation and interpret- ation of these fit statistics were previously described by Y ¼ bX ð3Þ hk hk Mayer (1941), Gadow & Hui (1999), Ruiz-Peinado et al. (2011), and Goicoa et al. (2011). where b ¼½ b b and X ¼ if b ≠ 0; 1 D H 0 1 hk hk 0 hk hi Among the different model forms tested (Y = b +b D , 0 1 T 2 2 and b ¼½ 0 b ¼ BEF and X ¼ 0 D H ff hk 1 c hk Y=b +b D +b Hand Y=b +b D H, where b and b hk 0 1 2 0 1 0 1 2 T are regression coefficients, D is the DBH and H is the tree ¼ D H ff if b =0. denotes matrix transpose. hk 0 4 hk height), the model form Y = b +b D H was the best for 8 0 1 The biomass of plot h (Ŷ ) is estimated by summing tree components and for the whole tree biomass, and the the individual biomass (Ŷ ) values of the n trees in plot hk h second best for the remaining tree components, as judged h. Dividing Ŷ by plot size a gives biomass Ŷ on an area by the goodness of fit statistics described above. Therefore, basis: to allow all tree components and whole tree biomass nh models to have the same regressors, and thus achieve ad- b X hk ditivity, this model form was generalized for all tree com- h k¼1 Y ¼ ¼ ð4Þ ponents and whole tree biomass models. a a Linear weighted least squares were used to address where k =1, 2, …, n , and h =1, 2, …, n , n = number of heteroscedasticity. The weight functions were obtained h p p th plots in the sample, and n = number of trees in the h by iteratively finding the optimal weight that homogenised plot. the residuals and improved other fit statistics. Among the 2 2 nh tested weight functions (1/D, 1/D , 1/DH, 1/D H), the hk best weight function was found to be 1/D H for all tree k¼1 components and whole tree biomass models. Although Denoting S ¼ , Eq. (4) can be rewritten as: a Magalhães Forest Ecosystems (2015) 2:28 Page 4 of 12 ^ where S = covariance of b and b , S = variance of b b i j b b Y ¼ bS ð5Þ i j i i ðÞ S −S S −S hi i hj j h¼1 b , S ¼ = covariance of Z and Z , i z z i j i j n ðÞ n −1 n h p p where S ¼½ S S .Where S ¼ and S ¼ h h0 h1 h0 h1 and S = variance of Z . z z i nh nh i i X X 2 2 Note that if b = 0 (and then b =BEF ), S ¼ 0and D H D H ff 0 1 c b b i j hk hk hk hk k¼1 k¼1 S ¼ 0, therefore, S ¼ S and S ¼ S .Conse- z z bb b b zz z z i j 1 1 1 1 if b ≠ 0; and S =0 and S ¼ 0 h0 h1 a a quentely, VAR ¼ BEF S BEF þ Z S Z t c Z Z c 1 b b 1 1 1 1 1 if b = 0. which is equal to: The biomass stock Ȳ (average biomass per hectare) is estimated by summing the biomass Ŷ of each plot (area 2 2 VAR ¼ BEF S þ Z S ð11Þ basis) and dividing it by the number of plots n : t Z Z b b c 1 1 1 1 1 bS The square roots of Eqs. (8, 11) are the total standard Y ¼ ð6Þ errors (SE) of Ȳ, the square roots of the first compo- nents of Eqs. (8, 11) are the SEs of the first phase, and Now, denoting Z ¼ , Eq. (6) can be rewritten as the square roots of the second components of the same follows: equations are the SEs of the second phase of the relevant methods of estimating biomass stock. Y ¼ bZ ð7Þ In this study, the error of Ȳ of the first and second T T sampling phases, and of both phases combined is where Z ¼½ Z Z if b ≠ 0; and Z ¼½ 0 Z ¼ Z 0 1 1 1 expressed as the percent SE of the relevant phase or both if b = 0. phases combined, obtained by dividing the relevant SE by Recall that b is the row vector of the estimates from Ȳ and multiplying by 100. However, in some cases, the the second sampling phase (regression coefficients or error is expressed as the variance of Ȳ, especially where BEF values), and Z is the column vector of the estimates the proportional influence of a particular source of error from the first phase. needs to be known, because, unlike the SEs, the variances Eqs. (2, 3, 4, 5, 6, 7) were applied to estimate biomass of the first and second phases are additive (sum to total stock of each tree component and whole tree. variance) (Cunia 1990). Biomass stock [Eq. (7)] is estimated by combining the As said previously, the error of the first sampling estimates of the first and second phases (Z and b, respect- phase results from random plot selection and variability, ively). Two main sources of error must be accounted for and that from the second phase results from biomass in this calculation, that resulting from plot-level variability model (either regression or BEF model). McRoberts and (first sampling phase) and that from biomass equation: Westfall (2015), Henry et al. (2015), Temesgen et a.l either regression or BEF equation (second phase). (2015), and Picard et al. (2014) distinguish four sources Cunia (1965, 1986a, 1986b, 1990) demonstrated that the of errors (surrogate of uncertainty) in model prediction: total variance of Ȳ (mean biomass per hectare) can be esti- (1) model misspecification (also known as statistical mated by Eq. (8): model; i.e.: error due to model selection (Cunia 1986a)), VAR ¼ VAR þ VAR t 1 2 (2) uncertainty in the values of independent variables, T T ¼ b S b þ Z S Z ð8Þ ZZ bb (3) uncertainty in the model parameter estimates, and (4) residual variability around model prediction. where VAR and VAR are variance components from 1 2 The first source of error in model prediction arises the first and second sampling phases, respectively; S zz from the fact that changing the model will generally represents the variance–covariance matrix of vector Z ; change the estimates. Here, this error is expected to be and S represents the variance–covariance matrix of bb negligible as, in general, the predictors explained a large vector b. For this specific case, S and S are given in bb zz portion of the variation in biomass and because the models Eqs. (9, 10): were associated to a small error (CVr) (Table 1). In fact, ac- cording to Cunia (1986a) and McRoberts and Westfall S S b b b b 0 0 0 1 S ¼ ð9Þ (2015), when the statistical model used fits reasonably well bb S S b b b b 0 1 1 1 the sample data, the statistical model error is generally small and can be ignored. The second source of error is quantified by Magalhães and Seifert (2015b). The third S S z z z z 0 0 0 1 source of error is expressed by the parameter variance- S ¼ ð10Þ zz S S z z z z 0 1 1 1 covariance matrix, S . In this study, this source of error is bb Magalhães Forest Ecosystems (2015) 2:28 Page 5 of 12 Table 1 Regression coefficients (± SE), BEF values (± SE) and the fit statistics for each tree component and for total biomass −3 2 # Tree component b (± SE) b (± SE) or BEF (Mg m ) (± SE) R (%) S (Kg) CVr (%) MR (%) 0 1 y.x Regression model b c 1 Taproot + stump 1.3122 (±36.69 %) 0.0045 (±4.44 %) 87.93 7.94 33.57 1.1612 a c 2 Lateral roots – 1.0600 (±43.02 %) 0.0051 (±3.92 %) 91.09 8.05 33.47 1.7376 ns c 3 Root system (1 + 2) 0.2522 (±251.15 %) 0.0097 (±2.06 %) 95.00 9.59 20.10 – 0.0709 ns c 4 Stem wood 0.6616 (±173.08 %) 0.0251 (±1.59 %) 97.52 19.66 15.84 0.0871 ns c 5 Stem bark 0.1895 (±186.28 %) 0.0028 (±3.57 %) 84.41 4.97 34.97 0.2638 ns c 6 Stem (4 + 5) 0.8511 (±147.84 %) 0.0279 (±1.79 %) 97.58 21.89 15.83 0.1029 ns c 7 Branches – 0.4569 (±332.74 %) 0.0114 (±5.26 %) 82.14 27.54 49.55 0.7460 c c 8 Foliage 0.7602 (±15.85 %) 0.0004 (±10.00 %) 49.41 1.86 66.21 1.5472 ns c 9 Crown (7 + 8) 0.3033 (±515.66 %) 0.0118 (±5.08 %) 82.36 25.11 43.01 – 0.3190 ns c 10 Shoot system (6 + 9) 1.1544 (±149.39 %) 0.0398 (±1.51 %) 97.75 31.07 15.80 – 0.0364 ns c 11 Whole tree (3 + 10) 1.4066 (±156.29 %) 0.0494 (±1.62 %) 97.64 34.92 14.29 – 0.0440 BEF model 1 Taproot + stump 0.0000 0.1407 (±3.53 %) 80.96 8.34 35.26 4.3080 2 Lateral roots 0.0000 0.1162 (±4.43 %) 80.11 10.75 44.70 2.7686 3 Root system (1 + 2) 0.0000 0.2569 (±2.66 %) 92.36 11.49 24.08 3.6116 4 Stem wood 0.0000 0.6569 (±1.04 %) 98.54 16.72 13.48 0.0755 5 Stem bark 0.0000 0.0765 (±3.81 %) 77.52 5.10 35.92 5.5460 6 Stem (4 + 5) 0.0000 0.7334 (±0.95 %) 98.85 18.77 13.57 0.0600 7 Branches 0.0000 0.2928 (±5.20 %) 74.54 29.10 52.35 2.7087 8 Foliage 0.0000 0.0242 (±10.60 %) 36.17 2.93 104.21 2.7751 9 Crown (7 + 8) 0.0000 0.3170 (±5.05 %) 76.34 28.89 49.48 2.7138 10 Shoot system (6 + 9) 0.0000 1.0504 (±1.65 %) 95.05 36.61 18.61 4.6507 11 Whole tree (3 + 10) 0.0000 1.3072 (±1.71 %) 95.06 45.67 18.69 4.4466 c b a SE standard error (%), “ ” = significant at α = 0.001; “ ” = significant at α = 0.01; “ ” = significant at α = 0.05; ns = not statistically significant at α = 0.05; the major components and their values are indicated in bold font expressed by the standard errors of the regression parame- by Eq. (12) using an independent sample of 37 trees ters or of theBEF values, as theyare thesquareroots ofthe (trees not included in fitting the models): respective variances obtained from the variance-covariance X X matrix, S . The fourth source (residual variability around PB − OB bb k k BiasðÞ % ¼ 100 ð12Þ model prediction) is here expressed as coefficient of vari- PB ation of residuals (CVr), as it measures the dispersion be- tween the observed and the estimated values of the model, where PB and OB represent, respectively, the predicted k k indicates the error that the model is subject to when is used th and observed biomass of the c compontent of the k tree. for predicting the dependent variable. As described above, the regression-based biomass is Therefore, the methods of estimating biomass under 2 estimated by the model form Y = b + b D H [kg] and the 0 1 study (regression and BEF models) were compared with BEF-based one is estimated by Y ¼ BEF v ¼ D hk regard to the following sources of errors: (1) random plot π 2 H ff [Mg], which is equal to Y ¼ D H ff 1000 selection and variability, (2) biomass model, (3) model [kg], where as v and H are expressed in m and m, hk parameter estimates, and (4) residual variability around respectively, D must be converted to m, which makes model prediction. The first constitutes the error of the π 2 BEF-based biomass (in kg) to be estimated as Y ¼ D first sampling phase and the second constitutes the error 40000 π 2 H ff 1000 ¼ D H ff if D is expressed in cm. of the second phase which incorporates the third and fourth source of errors. From Table 1 it can be seen that 8 out of the 11 re- The percent biases resulting from regression equation gression equations have their intercepts not statistically based and from BEF-based estimates were determined siginicant at α = 0.05; therefore, the regression equation Magalhães Forest Ecosystems (2015) 2:28 Page 6 of 12 can be generelized as Y = b D H [kg] and the BEF model (CVr) are larger for BEF models, except for stem and BEFπff ~ ~ stem wood components. as Y ¼ b D H [kg], where b ¼ . Thus, to esti- 1 1 The regression equation based biomass stocks estimates mate the percentual difference between regression-based 2 were relatively larger than the BEF-based ones, except for and BEF-based biomasses at a given D H, b and b 1 1 foliage (Table 2). For example, the regression equation were contrasted; i.e.: the percentual magnitude of b in based BGB, AGB and whole tree biomass stocks were 7.7, relation to b was taken as an indicative of how the dif- 8.5 and 8.3 % larger than the BEF-based ones. However, ferent models (regression and BEF models) estimate bio- the proportion of the whole tree biomass allocated to each mass from a given D H. Additionally, the average b and tree component is similar in either method; for instance, b for all components at given D H were compared BGB, stem, and crown biomass accounted for 20, 56 and using Student’s t-test. 24 %, respectively, to whole tree biomass for both Furthermore, the estimation errors (defined as the per- methods. Thepropertyof additivityisachievedin both centual difference between predicted and observed biomass methods, for the whole tree biomass and for all major values) of the individual trees from 2014 for each method tree components. This is so because for each particular of estimating biomass were plotted against those trees’ D H method (regression or BEF), all tree component models to evaluate the under or overestimation associated to each used the same predictors (DBH and H for regression method. Farther, the average errors at given D H per tree and stem volume for BEF models). (for each method) were compared using Student’s t-test. All Overall, the percent SEs of the first sampling phase the statistical analyses were performed at α = 0.05. (error resulting from plot selection and variability) of the BEF-based biomass estimates were slightly and some- Results times nigligibly larger than those obtained using regres- For all tree components and whole tree, except foliage, sion equations (Table 3), except for 2 tree components the variation of biomass explained by predictor variable(s) (lateral roots and branches) where the percent SEs were ranged 82.14 to 97.75 % for regression models and from relatively smaller. In the second sampling phase consid- 74.54 to 98.85 % for BEF models (Table 1). In general, the erable differences in percent SEs were found; BEF-based variation of biomass explained by the predictor variable(s) estimates exhibited smaller percent SE in 6 tree compo- was larger in regression models than in BEF ones, except nents and larger ones in the remaining five. The total for stem and stem wood (Table 1). Less than half of the percent SEs (both phases combined) were also negligibly variation of foliage biomass was explained by the predictor different between the two methods of estimating biomass variable(s). All tree components presented non-significant stocks, except for foliage where a substantial difference MRs. The plots of the residuals presented no particular was observed. Although, the average tree component bio- trend (refer to Magalhães and Seifert (2015a, b)); the clus- masses obtained by either method were slightly different ter of points was contained in a horizontal band, with the (Table 2), they fell in the 95 % confidence interval of any residuals evenly distributed under and over the axis of ab- method (Table 3). scissas, meaning that there were not model defects. The percent SE of the first phase is a result of plot se- The errors due to model parameter estimates (SE) and lection and variability, and that of the second phase is a those due to residual variability around model prediction result of biomass models (either regression or BEF models). Table 2 Regression equations based and BEF-based tree component biomass −1 −1 # Tree component Regression equation based biomass (Mg ha ) BEF-based biomass (Mg ha ) 1 Taproot + stump 16.8211 16.4818 2 Lateral roots 15.7750 13.6174 3 Root system (1 + 2) 32.5961 30.0992 4 Stem wood 84.7881 76.9789 5 Stem bark 9.7662 8.9609 6 Stem (4 + 5) 94.5543 85.9398 7 Branches 37.5688 34.3077 8 Foliage 2.3322 2.8375 9 Crown (7 + 8) 39.9010 37.1452 10 Shoot system (6 + 9) 134.4553 123.0850 11 Whole tree (3 + 10) 167.0517 153.1841 The major components and their values are indicated in bold font Magalhães Forest Ecosystems (2015) 2:28 Page 7 of 12 −1 Table 3 Absolute standard errors (Mg ha ), percent standard errors, and 95 % confidence limits of the estimates of tree component biomass stocks for each sampling phase using regression equations and BEFs −1 # Tree component SE SE SE SE (%) SE (%) SE (%) 95 % CI (Mg ha ) 95 % CI (%) 1 2 t 1 2 t Measures of precision for regression equations based biomass 1 Taproot + stump 0.7188 0.5592 0.9107 4.2733 1.8587 5.4139 ±1.8214 ±10.8279 2 Lateral roots 0.7837 0.5308 0.9465 4.9680 1.7861 6.0003 ±1.8931 ±12.0005 3 Root system (1 + 2) 1.4838 0.7357 1.6562 4.5520 1.6607 5.0809 ±3.3124 ±10.1618 4 Stem wood 3.8593 1.3301 4.0821 4.5517 2.0867 4.8145 ±8.1642 ±9.6289 5 Stem bark 0.4392 0.4069 0.5987 4.4976 1.6952 6.1308 ±1.1975 ±12.2616 6 Stem (4 + 5) 4.2984 1.4616 4.5401 4.5460 2.2593 4.8016 ±9.0802 ±9.6032 7 Branches 1.7476 1.7660 2.4845 4.6516 8.3019 6.6133 ±4.9691 ±13.2266 8 Foliage 0.1024 0.1399 0.1734 4.3902 0.8396 7.4346 ±0.3468 ±14.8692 9 Crown (7 + 8) 1.8166 1.8168 2.5692 4.5527 8.2723 6.4389 ±5.1383 ±12.8777 10 Shoot system (6 + 9) 6.1150 2.0033 6.4348 4.5480 2.9849 4.7858 ±12.8695 ±9.5716 11 Whole tree (3 + 10) 7.5988 2.5537 8.0164 4.5487 3.9039 4.7988 ±16.0328 ±9.5975 Measures of precision for BEF-based biomass 1 Taproot + stump 0.7565 0.5818 0.9543 4.5898 3.5300 5.7903 ±1.9087 ±11.5805 2 Lateral roots 0.6250 0.6029 0.8684 4.5898 4.4277 6.3773 ±1.7369 ±12.7546 3 Root system (1 + 2) 1.3815 0.7996 1.5962 4.5898 2.6566 5.3031 ±3.1924 ±10.6062 4 Stem wood 3.5331 0.8015 3.6229 4.5898 1.0411 4.7064 ±7.2458 ±9.4127 5 Stem bark 0.4113 0.3418 0.5348 4.5898 3.8147 5.9680 ±1.0696 ±11.9361 6 Stem (4 + 5) 3.9444 0.8141 4.0276 4.5898 0.9473 4.6865 ±8.0551 ±9.3730 7 Branches 1.5746 1.7159 2.3289 4.5898 5.0015 6.7883 ±4.6578 ±13.5766 8 Foliage 0.1302 0.3008 0.3278 4.5898 10.6013 11.5522 ±0.6556 ±23.1044 9 Crown (7 + 8) 1.7049 1.8741 2.5335 4.5898 5.0452 6.8206 ±5.0670 ±13.6412 10 Shoot system (6 + 9) 5.6493 2.0288 6.0025 4.5898 1.6483 4.8767 ±12.0051 ±9.7535 11 Whole tree (3 + 10) 7.0308 2.6231 7.5041 4.5898 1.7124 4.8988 ±15.0083 ±9.7975 Subscripts 1 and 2 indicate the first and second sampling phases, respectively; subscript t indicates the total standard error (SE) for a given component; the major components and their values are indicated in bold font From Table 4, it is noted that for both methods, the per- are considerably smaller than those from regression centage of the total error (as total variance) attributed to based ones. Recall that BEF models for stem wood and firstphase (plot selection)islargerthanthatattributedto stem were found to be associated to larger R , smaller second phase (biomass models), except for the foliage, percentage of total error (as variance) attributed to bio- branches and crown. The percentage of the total error mass model, smaller errors due to model parameter esti- (as total variance) attributed to BEF models is larger than mates and smaller errors due to residual variability around that attributed to regression models in all tree compo- model prediction than the regression models. nents, except for stem wood, stem bark and stem (stem It was found that at a given D H, the regression-based bark + stem wood). The percentage of the total error biomass estimates tended to be considerably larger than (as total variance) attributed to BEF model for stem wood the BEF-based ones (Table 6), supporting the finding from and stem is more than twice as small as that attributed to Table 2. However, it is worth mentioning that the percentual regression model. difference between the regression-based and BEF-based bio- The BEF-based biomass estimates were found to be mass estimates at a given D Hfor taproot+stump, lateral more biased than the regression-based ones in 6 out of roots, and foliage are overestimated, as for those com- 11 tree components (Table 5). Overall, regression equa- ponents the intercepts are statistically significant and tion based biomasses tended to be larger than the ob- then should not be removed from the model. For ex- served biomasses and the BEF-besed ones tended to be ample, it was expected the regression-based biomass smaller than the observed ones. As expected, the per- estimate at a given D H for the taproot + stump to be cent biases for stem wood and stem BEF-based biomass larger than the BEF-based one, therefore in accordance Magalhães Forest Ecosystems (2015) 2:28 Page 8 of 12 Table 4 Percentage of total error (as variance) attributed to each sampling phase Regression equation based biomass BEF-based biomass # Tree component Percentage of variance attributed Percentage of variance Percentage of variance attributed Percentage of variance to the first phase (plot selection attributed to the second to the first phase (plot selection attributed to the second and variability) phase (regression model) and variability) phase (BEF model) 1 Taproot + stump 62 38 63 37 2 Lateral roots 69 31 52 48 3 Root system (1 + 2) 80 20 75 25 4 Stem wood 89 11 95 5 5 Stem bark 54 46 59 41 6 Stem (4 + 5) 90 10 96 4 7 Branches 49 51 46 54 8 Foliage 35 65 16 84 9 Crown (7 + 8) 50 50 45 55 10 Shoot system (6 + 90 10 89 11 9) 11 Whole tree (3 + 10) 90 10 88 12 The major components and their values are indicated in bold font to the Table 2 (yielding a negative difference); however, statistical different from zero (p-value = 0.51). On the the exclusion of the intercept caused the BEF-based other hand, the plot of the errors show that the BEF biomass estimate at a given D H to be larger, causing a model underestimates the biomass, a finding confirmed positive difference. Accordingly, the really differences be- by Student’s t-test (average error = −8.60, p-value = 0.0007). tween the regression-based and the BEF-based biomass estimates at a given D H for lateral roots and foliage Discussion are smaller than those presented in the Table 6. Using This study compares two commonly used methods of Student’s t-test the average biomass estimates by each estimating tree and forest biomass: regression equations method at a given D H are found to be statistically and biomass expansion factors. This is a unique study different (p-value = 0.01). for many reasons: (1) the precision and bias associated The estimation errors per tree plotted against the re- with each method of estimating biomass are critically com- spective D H values (Fig. 1) for the whole tree show that pared; the errors associated with biomass estimates are the positive and negative errors of regression model cancel rarely evaluated carefully (Chave et al. 2004); (2) the com- each other, tending to average zero; in fact, the Student’s t parison involved 11 tree components, including BGB, test showed that the average percent error (1.34 %) is not which is rarely studied (GTOS 2009); (3) in turn, BGB was divided into 2 root components: taproot and lateral roots. Table 5 Comparision of bias between regression equation Many biomass studies include only AGB not breakdown based and BEF-based biomass estimates in further components (e.g. Overman et al. 1994; Grundy a b # Tree component Bias (%) Bias (%) 1995; Eshete and Ståhl 1998; Pilli et al. 2006; Salis et al. 1 Taproot + stump – 3.3436 – 5.6745 2006; Návar-Cháidez 2010; Suganuma et al. 2012; Sitoe et 2 Lateral roots – 3.3643 13.8733 al. 2014; Mason et al. 2014), ignoring the fact that different tree components have distinguished uses and decompos- 3 Root system (1 + 2) – 3.3540 4.1660 ition rates, affecting differently the storage time of carbon 4 Stem wood 10.0738 1.3651 and nutrients (Magalhães and Seifert 2015a). Aware of 5 Stem bark – 9.3876 – 1.4220 that, here, the AGB is divided into 6 tree components (fo- 6 Stem (4 + 5) 8.9983 0.3591 liage, branches, crown, stem wood, stem bark, and stem). 7 Branches – 9.4311 0.7147 Few studies have considered BGB (e.g. Kuyah et al. 8 Foliage – 23.2792 – 81.7205 2012; Mugasha et al. 2013; Green et al. 2007; Ryan et al. 2010; Ruiz-Peinado et al. 2011; Paul et al. 2014); in most 9 Crown (7 + 8) – 10.0298 – 2.8493 of those studies the root system was not fully excavated 10 Shoot system (6 + 9) – 2.5149 5.7208 (Green et al. 2007; Ryan et al. 2010; Ruiz-Peinado et al. 11 Whole tree (3 + 10) – 2.6778 5.4193 2011; Kuyah et al. 2012; and Paul et al. 2014), the exca- Superscripts a and b indicate biases related to regression equations based and vation was done to a certain predefined depth or the fine BEF-based biomass estimates, respectively; the major components and their values are indicated in bold font roots were not considered; or a sort of sampling Magalhães Forest Ecosystems (2015) 2:28 Page 9 of 12 Table 6 Comparision between regression-based and BEF-based models for those tree components (stem wood and stem) biomass at a given D H were associated to larger R , smaller biases, smaller errors # Tree component b b Difference (%) due to model parameter estimates and smaller errors due 1 1 to residual variability around model prediction than the 1 Taproot + stump 0.0045 0.0049 9.4855 regression models. Therefore, although it has been main- 2 Lateral roots 0.0051 0.0041 −20.1840 tained that biomass regression equations yield the most 3 Root system (1 + 2) 0.0097 0.0090 −7.2427 accurate estimates than BEFs (IPCC 2003; Jalkanen et al. 4 Stem wood 0.0251 0.0230 −8.3224 2005; Zianis et al. 2005; António et al. 2007; Soares and 5 Stem bark 0.0028 0.0027 −4.3334 Tomé 2012), this might not be true when stem and stem 6 Stem (4 + 5) 0.0279 0.0257 −7.9220 wood components are concerned. This is so because the stem BEF value is computed by dividing the stem biomass 7 Branches 0.0114 0.0103 −10.0394 by stem volume, which makes the stem BEF value to be 8 Foliage 0.0004 0.0008 112.0524 similar to stem wood density (specific gravity) and thus 9 Crown (7 + 8) 0.0118 0.0111 −5.9007 more realistic (than models using only DBH and tree 10 Shoot system (6 + 9) 0.0398 0.0368 −7.5541 height) when using it to convert stem volume to stem bio- 11 Whole tree (3 + 10) 0.0494 0.0458 −7.3058 mass, as biomass is a function of wood density (Ketterings The major components and their values are indicated in bold font et al. 2001). As for stem wood biomass, since the differ- ence between stem wood and stem biomass is negligible. procedure was used (Kuyah et al. 2012; Mugasha et al. On the contrary, using stem volume to obtain any other 2013). These procedures of estimating BGB lead to tree component biomass, through BEF value, is not realis- underestimation or to less accurate estimates (Mokany tic, since the density varies from component to compo- et al. 2006; Mugasha et al. 2013). Furthermore, studies nent, leading to less accurate and less precise estimates. that have breakdown BGB into further root compo- This is aggravated for the non-woody components, where nents are limited. the density value may differ greatly from the stem density Theonlystudies availablethatcompare regression equa- value. In fact, it has been noted here that the BEF-based tions based and BEF-based biomass estimates are those by foliage biomass is associated with the largest percent error Jalkanen et al. (2005) and Petersson et al. (2012), which, (11.55 %), and that 84 % of that error is attributed to BEF however, did not consider BGB. The finding that the whole model (Table 4), besides being associated to the largest tree BEF-based biomass estimate was 8.3 % lower, with error due to model parameter estimates and due to re- slightly larger percent error than that based on regression sidual variability around model prediction (within and equation is in line with the finding by Jalkanen et al. between methods). (2005), which found that BEF-based AGB estimate was In this study, the average stem density value of A.john- −3 6.7 % lower. sonii trees was 754.42 Kg m and the average stem BEF −3 −3 It was verified here that the percentage of the total was 0.7334 Mg m (733.40 Kg m ). The small differ- error of biomass (as total variance) attributed to BEF ence of these estimates might be due to the fact that the model for stem wood and stem is more than twice as stem density was computed using saturated volume and small as that attributed to regression model; and that BEF the stem BEF value was computed using green volume. Fig. 1 Comparision of the estimation errors of the regression model and BEF model for the whole tree biomass Magalhães Forest Ecosystems (2015) 2:28 Page 10 of 12 The stem density obtained here is in line with that by small tree biomass (DBH <10 cm) is equivalent to 5 % of −3 Bunster (2006) (754 Kg m ) for the same tree species. large tree biomass. Nevertheless, in this study, the share of The errors of regression-based biomass estimates are small trees biomass to aboveground live biomass or to the same as those obtained by Magalhães and Seifert large trees biomass is expected to be very small than that (2015b) for the relevant tree components. However, the reported by Lugo and Brown (1992), Chave et al. (2003) errors of the BEF-based estimates were slightly different and Vicent et al. (2015) as the definition of small trees from those obtained by Magalhães and Seifert (2015c); (DBH <5 cm) considered here, include only part of the these differences might be attributed to the different ap- trees considered as small by those authors. proaches used to compute the errors. The regression-based biomass estimates could have Conclusions been more precise if non-linear regression models were The regression equation based BGB and AGB stocks were, −1 −1 used instead of linear ones, as biomass is better described approximately, 33.6 ± 3.3 Mg ha and 134.5 ± 12.9 Mg ha , by non-linear functions (Bolte et al. 2004; Ter-Mikaelian respectively.The BEF-basedBGB andAGB were,ap- −1 −1 and Korzukhin 1997; Schroeder et al. 1997; de Jong and proximately, 30.1 ± 3.2 Mg ha and 123.1 ± 12.0 Mg ha , Klinkhmer 2005; and Salis et al. 2006). However, the ap- respectively. proach of combining the errors from the first and second Overall, the regression equation based biomass stocks phases developed by Cunia (1986a) is limited to linear were found to be slightly larger, associated with relatively regression models, as using non-linear regression, the smaller errors and least biased than the BEF-based ones. expression of the error (as variance) may be so complex However, because stem BEF and stem wood BEFs are that may become extremely cumbersome to apply (Cunia equivalent to stem and stem wood densities (specific grav- 1986a). In the meantime, the linear models used here per- ities) and therefore, the equivalent biomasses computed formed satisfactorily; relatively lower performance was ob- directely by multiplying stem volume by stem or stem wood tained for foliage biomass model (R =49.41 %; CVr = density, the percentages of their total errors (as total vari- 66.21 %; MR = 1.55 %). Foliage biomass models have, usu- ance) attributed to BEF model were considerably smaller ally, shown relatively poor performance (Brandeis et al. than those attributed to biomass regression equations, 2006; Mate et al. 2014). as regression equations were based only on DBH and A combined-variable model (Y = b +b ×D H) was 0 1 stem height and ignored the stem density. used here to estimate tree component biomass. Silshi Abbreviations (2014) has referred that where compound derivatives of AGB: Aboveground biomass; BGB: Belowground biomass; DBH: Diameter at DBH and H are included there is no unique way to par- breast height; H: Tree height; BEF: Biomass expansion factor; MR: Mean residual; tition the variance in the response. However, the Monte CVr: Coefficient of variation of residuals; R : Coefficient of determination; SE: Standard error. Carlo error propagation approach can be applied to esti- mate the percent contribution of each variable (DBH Competing interests and H) measurement error to the error of biomass esti- The author declares that he has no competing interests. mate as performed by Magalhães and Seifert (2015b) Acknowledgments and Chave et al. (2004) or using Bayesian approach as This study was funded by the Swedish International Development Cooperation done by Molto et al. (2012). Agency (SIDA). Thanks are extended to Professor Thomas Seifert for his It has been maintained here that the error due to contribution in data collection methodology and to Professor Almeida Sitoe for his advices during the preparation of the field work. I would also model misspecification was ignored because it is expected like to thank Professor Agnelo Fernandes and Madeirarte Lda for financial to be negligible as overall the models fitted reasonably well and logistical support. the sample data. However, the foliage biomass models Received: 31 May 2015 Accepted: 13 October 2015 might be associated with a large model misspecification error as their predictors explained less than half of the variation in biomass, especially the foliage BEF model. References The current biomass estimates disregarded smaller and Antonio N, Tome M, Tome J, Soares P, Fontes L (2007) Effect of tree, stand and site variables on the allometry of Eucalyptus globulus tree biomass. Can J For younger trees (DBH <5 cm), which may have led to under- Res 37:895–906 estimation, as those trees may have a significant contribu- Black K, Tobin B, Siaz G, Byrne KA, Osborne B (2004) Allometric regressions for an tion to forest biomass stock and are reported to be very improved estimate of biomass expansion factors for Ireland based on a Sitka spruce chronosequence. 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Silva Fennica, Monographs 4. Submit your manuscript to a journal and beneﬁ t from: 7 Convenient online submission 7 Rigorous peer review 7 Immediate publication on acceptance 7 Open access: articles freely available online 7 High visibility within the ﬁ eld 7 Retaining the copyright to your article Submit your next manuscript at 7 springeropen.com
"Forest Ecosystems" – Springer Journals
Published: Dec 1, 2015
Keywords: Ecology; Ecosystems; Forestry
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