research article biomass modelling of androstachys johnsonii prain: a comparison...

Research ArticleBiomass Modelling of Androstachys johnsonii PrainA Comparison of Three Methods to Enforce Additivity

Tarquinio Mateus Magalhatildees12 and Thomas Seifert2

1Departamento de Engenharia Florestal Universidade Eduardo Mondlane Campus UniversitarioEdifıcio No 1 257 Maputo Mozambique2Department of Forest and Wood Science University of Stellenbosch Stellenbosch 7602 South Africa

Correspondence should be addressed to Tarquinio Mateus Magalhaes tarqmagyahoocombr

Received 26 January 2015 Revised 23 March 2015 Accepted 5 April 2015

Academic Editor Piermaria Corona

Copyright copy 2015 T M Magalhaes and T Seifert This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Three methods of enforcing additivity of tree component biomass estimates into total tree biomass estimates for Androstachysjohnsonii Prain were studied and compared namely the conventional (CON) method (a method that consists of using the sameindependent variables for all tree componentmodels and for total treemodel and the sameweights to enforce additivity) seeminglyunrelated regression (SUR) with parameter restriction and nonlinear seemingly unrelated regression (NSUR) with parameterrestriction The CON method was found to be statistically superior to any other method of enforcing additivity yielding excellentfit statistics and unbiased biomass estimates The NSUR method ranked second best but was found to be biased The SUR methodwas found to be the worst it exhibited large bias and had a poor fit for the biomass Therefore we recommend that only theCON and NSUR methods should be used for further estimates provided that their limitations are considered that is exclusion ofcontemporaneous correlations for the CONmethod and consideration of the significant bias of the NSUR method

1 Introduction

In the early 1960sAndrostachys johnsonii Prain (A johnsonii)had already been reported to be almost completely restrictedto Mozambique [1] presumably due to overexploitation Fivedecades later there is still a lack of studies on this speciesin any branch of forest science particularly tree allometrysupporting that this species may indeed be restricted toMozambique Moreover in Mozambique biomass modelshave rarely been reported for any tree species and no suchmodels have been described for A johnsonii Isolated studiesin Mozambique have focused on Miombo woodlands andsome forest plantations and are often part of research thesesor forestry projects therefore the results are not alwaysmade public Generally such studies have only considered theaboveground biomass and have not included a breakdown offurther tree components

A johnsonii woodlands (Mecrusse) are very importantBesides being restricted to Mozambique [1] Mecrusse hasimportant socioeconomic value to local communities which

use stakes of A johnsonii in the construction of homesshelters and furniture and sell them for income generationAt the global scale Mecrusse is reported to be a tippingpoint in regional ecological and socioeconomic development[2] hence the importance of modelling and estimating itsbiomass

The estimation of aboveground biomass is importantto predict the amount of carbon that is sequestered [3ndash5] to assess nutrient cycling and fluxes and energy woodpotentials [4 6] and to provide estimates for the differenttree components [5] These types of estimates are importantfor several reasons as follows (i) stem wood biomass isan important quantity because this component is the onlyone used in the forest industry and the carbon thereforeremains stored for a long time and is not released intothe atmosphere (ii) in many species branches and foliageare left in the forest and decompose releasing CO

2and

nutrients (iii) in some species especially broadleaf speciesthe branches are collected by members of local communitiesfor use as firewood which will result in release of CO

2

Hindawi Publishing CorporationInternational Journal of Forestry ResearchVolume 2015 Article ID 878402 17 pageshttpdxdoiorg1011552015878402

2 International Journal of Forestry Research

Table 1 Summary statistics for the independent and dependent variables

Variable Minimum Q025 Median Average Q075 Maximum SD CV ()DBH (cm) 500 1100 1750 1759 2400 3200 751 4272Total tree height119867 (m) 569 1121 1277 1232 1390 1600 214 1735Crown height CH (m) 070 374 516 505 615 992 201 3986Live crown length LCL (m) 110 550 705 727 890 1350 247 3405Belowground biomass (kg) 255 1166 3604 4773 7349 16210 4121 8633Stem wood biomass (kg) 495 3051 10318 12407 19762 35735 9950 8020Stem bark biomass (kg) 068 352 1117 1420 2260 5580 1237 8714Crown biomass (kg) 304 1368 3736 5839 8044 21669 5908 10117Total tree biomass (kg) 1248 5990 20439 24439 36823 75257 20433 8361Q025 = first quartile Q075 = third quartile SD = standard deviation CV = coefficient of variation

(iv) the stump and root system are left in the forest allowingthe stump to either sprout (regrow) continuing the seques-tration process or decompose along with the roots releasingCO2and nutrients and (v) in some tree species belowground

biomass can account for more than one-third of the totalbiomass [7] Hence it is critical to estimate the biomass ofall tree components as well as the total tree biomass in orderto assess the global carbon balance

However the biomass estimates of the considered treecomponents often do not sum to the estimate of the totaltree biomass and a desired and logical feature of the treecomponent regression equations is that the predictions of thecomponents sum to the prediction for the total tree Thisfeature is called additivity Various authors such as Goicoa etal [5] Kozak [8] Cunia [9] Cunia and Briggs [10 11] Jacobsand Cunia [12] Parresol [4 13] and Carvalho and Parresol[14] have proposed andor discussed various methods toensure the property of additivity

The objective of this study was to fit independent lin-ear and nonlinear tree component and total tree biomassmodels and compare three methods of enforcing the prop-erty of additivity (the conventional (CON) method seem-ingly unrelated regression (SUR) with parameter restrictionand nonlinear seemingly unrelated regression (NSUR) withparameter restriction) for A johnsonii tree species

TheCONmethod consists of using the same independentvariables for all tree component models and for total treemodel and the same weights to enforce additivity [4] TheSUR and NSUR methods consist in first fitting and selectingthe best linear and nonlinear models respectively for eachtree component The total tree model is a function of theindependent variables used in each component model Thenall models including the total are fitted again simultaneouslyusing joint-generalized least squares under the restriction ofthe coefficients of regression which ensures the additivityproperty [4]

2 Materials and Methods21 Study Area Mecrusse is a forest type where the mainspecies many times the only one in the upper canopy is Ajohnsonii [15]

In Mozambique Mecrusse woodlands are mainly foundin Inhambane and Gaza provinces and in MassangenaChicualacuala Mabalane Chigubo Guija Mabote Fun-halouro Panda Mandlakazi and Chibuto districts Theeastern-most Mecrusse patches covering the last five dis-tricts were defined as the study area The study area had anextension of 4502828 ha [16] of which 226013 ha (5) wascovered by Mecrusse woodlands

The climate is dry and tropical throughout the study areaexcept in the west part of the Panda district and the southwestpart of the Mandlakazi district where the climate is humidand tropical [16ndash21] The climate has two seasons the warmor rainy season from October to March and the cool or dryseason fromMarch to September [17ndash21]

The mean annual temperature is generally greater than24∘C and the mean annual precipitation varies from 400to 950mm [16ndash21] According to FAO classification [22]the soils in the study area are mainly Ferralic Arenosolscovering more than 70 of the study area [16] ArenosolsUmbric Fluvisols and Stagnic soils are also predominant inthe northern-most part of the study area [16]

The study area is characterized by a shortage of waterresources as well as precipitation thus of the five districtsthat made up the study area only the districts of Chibutoand Mandlakazi have water resources [16ndash21] either fromprecipitation or from lakes and rivers

22 Data Acquisition A total of 93 trees (2 to 6 per plot)selected across all size classes (Table 1) were destructivelysampled within 23 circular plots randomly located in thestudy area Diameter at breast height (DBH) total tree height(119867) crown height (CH) and live crown length (LCL) weremeasured on the felled trees Trees were divided into thefollowing tree components (1) root system (2) stem wood(3) stem bark and (4) crown Tree components were sampledand the dry weights were estimated as follows

221 Root System The stump height was predefined as being20 cm for all trees and considered as part of the taprootas recommended by Parresol [13] and because in largerA johnsonii trees this stump height (20 cm) is affected by

International Journal of Forestry Research 3

(a) (b)

(c) (d)

(e) (f)

Figure 1 Separation of lateral roots from the root collartaproot (a b and c) and removal of the taproot including the root collar and thestump (d e and f)

the root buttress therefore the root collar was also consid-ered part of the taproot The root system was divided into3 subcomponents fine lateral roots coarse lateral roots andtaproot Lateral roots with diameters at insertion point on thetaproot lt 5 cm were considered as fine roots and those withdiameters ge 5 cm were considered as coarse roots

First the root system was partially excavated to thefirst node using hoes shovels and picks to expose theprimary lateral roots (Figures 1(a)ndash1(c)) The primary lateralroots were numbered and separated from the taproot with achainsaw (Figures 1(b) and 1(c)) and removed from the soilone by one This procedure was repeated in the subsequentnodes until all primary roots were removed from the taprootand the soil Finally the taproot was excavated and removed(Figures 1(d)ndash1(f)) The complete removal of the root system

was relatively easy because 90 of the lateral roots of Ajohnsonii are located in the first node which is located closeto ground level (Figures 1(a)ndash1(d)) the lateral roots growhorizontally to the ground level and do not grow downwardsand because the taproots had at most only 4 nodes and atleast 1 node (at ground level)

Fresh weight was obtained for the taproot each coarselateral root and for all fine lateral roots A sample was takenfrom each subcomponent fresh weighed marked packed ina bag and taken to the laboratory for oven drying For thetaproot the samples were two discs one taken immediatelybelow the ground level and another from the middle of thetaproot For the coarse lateral roots two discs were also takenone from the insertion point on the taproot and another fromthe middle of it For fine roots the sample was 5 to 10 of


the fresh weight of all fine lateral roots Oven drying ofall samples was done at 105∘C to constant weight (ie toapproximately 0moisture content) hereafter referred to asdry weight

222 Stem Wood and Stem Bark Felled trees were scaledup to a 25 cm top diameter The stem was defined as thelength of the trunk from the stump to the height thatcorresponded to 25 cm diameter The remainder (from theheight corresponding to 25 cm diameter to the tip of thetree) was considered a fine branchThe stemwas divided intosections the first with 11m length the second with 17mand the remaining with 3m except the last whose lengthdepended on the length of the stem Discs were removed onthe bottom and top of the first section and on the top of theremaining sections that is discs were removed at heights of02m (stump height) 13m (breast height) and 3m and thesuccessive discs were removed at intervals of 3m to the topof the stem and their fresh weights were measured using adigital scale

Diameters over and under bark were taken from thediscs in the North-South direction (previouslymarked on thestanding tree) with the help of a ruler The volumes over andunder the bark of the stem were obtained by summing up thevolumes of each section calculated using Smalianrsquos formula[27 28] Bark volume was obtained from the differencebetween volume over bark and volume under bark

The discs were dipped in drums filled with water for itssaturation (3 to 4 months) and subsequent determination ofthe saturated volume and basic densityThe saturated volumeof the discs was obtained based on the water displacementmethod [29] usingArchimedesrsquo principleThis procedurewasdone twice before and after debarking hence we obtainedsaturated volume under and over the bark

Wood discs and respective barks were oven dried at 105∘Cto constant weight Basic density was obtained by dividingthe oven dry weight of the discs (with and without bark) bythe relevant saturated wood volume [27 30] Therefore twodistinct basic densities were calculated (1) basic density of thediscs with bark and (2) basic density of the discs without bark

We estimated the basic density at point of geometriccentroid of each section using the regression function ofdensity over height [31] This density value was taken asrepresentative of each section [31]

223 Crown The crown was divided into two subcompo-nents branches and foliage Primary branches originatingfrom the stem were classified in two categories primarybranches with diameters at the insertion point on the stemge 25 cm were classified as large branches and those withdiameters lt 25 cm were classified as fine branches

Large branches were sampled similarly to coarse rootsand fine branches and foliage were sampled similarly to fineroots All the leaves from each tree were collected and freshweighed together and a sample was taken for oven dryingThe subcomponents branches and foliage were not treatedas separated components because in the preliminary analysisthe weight of the foliage did not show significant variationwith DBH H CH and LCL exhibiting therefore poor fits

224 Tree Component Dry Weights Dry weights of coarseand fine roots large and fine branches and foliage wereobtained from the ldquofresh weightoven dry weightrdquo ratio ofthe respective samples by multiplying it by the relevantsubcomponent total fresh weight Dry weights of the rootsystem and crown were obtained by summing up the relevantsubcomponentsrsquo dry weights

Dry weights of each stem section (with and without bark)were obtained by multiplying respective densities by relevantstem section volumes Stem (wood + bark) and stem wooddry weights were obtained by summing up each sectionrsquos dryweight with and without bark respectively The dry weightof the stem bark was obtained from the difference betweenthe dry weights of stem and stem wood Finally the total treebiomass was obtained by adding the component dry weights

23 Data Analysis Several linear and nonlinear regressionmodel forms were tested for each tree component and forthe total tree using weighted least squares (WLS)The weightfunctions were obtained by iteratively finding the optimalweight that homogenises the residuals and improves otherfit statistics Independent tree component models were fittedwith the statistical software package R [32] and the functionslm and nls for linear models and nonlinear models (thelatter of which using the Gauss-Newton algorithm) The bestlinear and nonlinear biomass equations selected are given in(1) and (2) respectively Among the tested weight functions(1119863 11198632 1119863119867 1119863LCL 11198632119867 and 11198632LCL) thebest weight function was found to be 11198632119867 for all treecomponent equations (linear or nonlinear) Although theselected weight function might not be the best one among allpossible weights it is the best approximation found Consider

Roots = 1198870 + 11988711198632119867

Stem-wood = 1198870 + 11988711198632119867

Stem-bark = 1198870 + 11988711198632119867

Crown = 1198870 + 11988711198632LCL025

Total-tree = 1198870 + 11988711198632119867

(1)

Roots = 1198870 (1198632119867)1198872

Stem-wood = 119887011986311988711198671198872

Stem-bark = 119887011986311988711198671198872

Crown = 11988701198631198871LCL1198872

Total-tree = 1198870 (1198632119867)1198872

(2)

TheCONmethod used the same independent variables for alltree componentmodels and the total tree model and used thesame weight functions [4] achieving additivity automatically[5] For this method the most frequent best linear modelform in (1) among tree components was used for all othercomponents and for total tree biomass The most frequent


Table 2 Coefficients of regression of SUR using the system of the best linear models

Tree component Weight function 1198870(plusmnSE) 119887

1(plusmnSE) 119887

2(plusmnSE)

Roots 11198632119867 01404 (plusmn05950) 00046 (plusmn00002)

Stem wood 11198632119867 01025 (plusmn04193) 00070 (plusmn00001)

Stem bark 11198632119867 01076 (plusmn03150) 00001 (plusmn00001)

Crown 11198632119867 minus18559 (plusmn15017) 01124 (plusmn00044)

Total tree 11198632119867 minus15053 (plusmn18765) 00117 (plusmn00002) 01124 (plusmn00044)

ldquordquo = significant at 120572 ge 5 ldquo rdquo = not significant at any probability level

Table 3 Fit statistics of SUR using the system of the best linear models

Tree component Weight function Adj1198772 () 119878119910sdot119909

(kg) CV () MRSE (kg) MR (kg) 119894119894

2

SUR

Roots 11198632119867 5600 349040 731758 02750 03227 01503

Stem wood 11198632119867 2217 1166327 940069 05181 11685 17454

Stem bark 11198632119867 minus2922 181996 1281809 08488 01751 00432 10028

Crown 11198632119867 8150 285040 488144 14814 minus01298 01087

Total tree 11198632119867 6319 2495561 1021272 02332 15366 144049


model form in (1) is = 1198870+11988711198632119867 therefore the structural

system of equations for the CONmethod is given in

Roots = 11988710 + 119887111198632119867

Stem-wood = 11988720 + 119887211198632119867

Stem-bark = 11988730 + 119887311198632119867

Crown = 11988740 + 119887411198632119867

Total-tree = Roots + Stem-wood + Stem-bark + Crown

= (11988710+ 11988720+ 11988730+ 11988740)

+ (11988711+ 11988721+ 11988731+ 11988741)1198632119867

= 11988750+ 119887511198632119867

(3)

The SUR method consisted of first fitting and selecting thebest linear models for each tree component The total treemodel was a function (sum) of the independent variablesused in each tree component model Then all modelsincluding the total were fitted again simultaneously usingjoint-generalized least squares (also known as SUR) underthe restriction of the coefficients of regression which ensuredadditivity

The best linear model forms were found to be =1198870+ 11988711198632119867 for belowground stem wood and stem bark

biomasses and = 1198870+ 11988711198632LCL025 for the crown biomass

Summing up the best model forms from each tree compo-nent the model form obtained for the total tree biomass was = 1198870+ 11988711198632119867 + 119887

21198632LCL025

However the system of equations obtained by com-bining the best linear model forms per component underparameter restriction will not yield effective and preciseestimates because according to SAS Institute Inc [33] forSUR to be effective the models must use different regressors

This requirement is not verified as three of the four com-ponents have identical regressors Indeed according to Sri-vastava and Giles [34] applying SUR to system of the bestequations given above is of no benefit when the componentequations have identical explanatory variables Moreoveras stated by Greene [35] and Bhattacharya [36] a systemof linear SUR equations with identical regressors yieldsineffective estimates of coefficient vectors when compared toequation-by-equation ordinary least squares (OLS)

To eliminate the ineffectiveness caused by identicalregressors SUR was applied using second best regressionequations for belowground and stem wood biomasses suchthat the different tree component equations could havedifferent regressors The resulting system of equations ofbiomass additivity is given in (4) However the results of SURusing the best independent model forms are given in Tables2 and 3 for demonstration proposes of the ineffectivenesscaused by identical regressors Consider

Roots = 11988710 + 119887111198632+ 11988712119867

Stem-wood = 11988720 + 119887211198632

Stem-bark = 11988730 + 119887311198632119867

Crown = 11988740 + 119887411198632LCL025

Total = (11988710 + 11988720 + 11988730 + 11988740) + (11988711 + 11988721)1198632

+ 119887311198632119867 + 119887

411198632LCL025 + 119887

12119867

= 11988750+ 119887511198632+ 119887521198632119867 + 119887

531198632LCL025 + 119887

54119867

(4)

Note from the equations in (4) that the intercepts of alltree component biomass models are forced (constrainedrestricted) to sum to the intercept of the total tree biomassmodel the coefficients of regression for the regressor 1198632in the root system and stem wood biomass models are


Table 4 Standard error of the expected and predicted values for different methods

Statistic Absolute form Relative form

Standard error of the expected value for CON 119878 (119864 (1199100)) = 119878

119910sdot119909radic1

119899+(1199090minus 119909)2

SS119909

119878 (119864 (1199100)) =119878 (119864 (119910

0))

119910119894

times 100

Standard error of the predicted value for CON 119878 (1199100119894minus 119910) = 119878

119910sdot119909radic1 +1

119899+(1199090minus 119909)2

SS119909

119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100

Standard error of the expected value for SUR 119878 (119864 (1199100)) = radic119878

2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100

Standard error of the predicted value for SUR 119878 (1199100119894minus 119910) = radic119878

2

119910119894+ 2

SUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100

Standard error of the expected value for NSUR 119878 (119864 (1199100)) = radic119878

2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100

Standard error of the predicted value for NSUR 119878 (1199100119894minus 119910) = radic119878

2

119910119894+ 2

NSUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100

Sources Parresol [13] Lambert et al [23] Parresol andThomas [24] Snedecor and Cochran [25] and Yanai et al [26]SS119909 = sumof squares of the independent variable 119878119910sdot119909= standard deviation of the residuals1199090= particular value of119909 for which the expected value119910 is estimated119864(1199100) 119878

2

119910119894= estimated variance for the ith system equation on the observation 119910119894 119891119894(119887)

1015840 = a row vector for the ith equation from the partial derivatives matrix119865(119887) it is119891119894(119887) transposed Σ119887 = estimated covariancematrix of the parameter estimates119891119894(119887)= a column vector for the ith equation from the partial derivativesmatrix 119865(119887) 1205902SUR = SUR system variance 1205902NSUR = NSUR system variance 120590119894119894 = the (119894 119894) element of the covariance matrix of the residuals Σ (error covariancematrix) it is the covariance error of the ith system equation and 120595119894(120579119894) = estimated weight

constrained to sum to the coefficient of regression for 1198632in the total tree biomass model and the coefficients forthe regressors 119867 1198632119867 and 1198632LCL025 in the root systemstem bark and crown biomass models respectively areconstrained to be equal to the coefficients of the sameregressors in the total tree biomass model thereby achievingadditivity

The NSUR method had the same characteristics andwas performed using the same procedures as the SURmethod except that the system of equations was composed ofnonlinearmodels For reference please see Brandeis et al [3]Parresol [13] Carvalho and Parresol [14] and Carvalho [37]The system of equations (including the total tree biomass)obtained by combining the best nonlinear model forms percomponent under parameter restriction is given by

Roots = 11988710 (1198632119867)11988711

Stem-wood = 119887201198631198872111986711988722

Stem-bark = 119887301198631198873111986711988732

Crown = 1198874111986311988742LCL11988743

Total = 11988710 (1198632119867)11988711

+ 119887201198631198872111986711988722

+ 119887301198631198873111986711988732 + 1198874111986311988742LCL11988743

(5)

Note that the coefficients of regression of each regressorin each tree component model are forced (constrainedrestricted) to be equal to coefficients of the equivalentregressor in total tree model allowing additivity

The systems of equations in (4) and (5) were fittedusing PROC SYSLIN and PROC MODEL in SAS software

[33] respectively using the ITSUR option Restrictions (con-straints) were imposed on the regression coefficients by usingSRESTRICT and RESTRICT statements in PROC SYSLINand PROCMODEL procedures respectivelyThe start valuesof the parameters in PROCMODEL were obtained by fittingthe logarithmized models of each component in MicrosoftExcel

24 Model Evaluations and Comparison The best tree com-ponent and total tree biomass equation were selected byrunning various possible regressions on combinations of theindependent variables (DBH 119867 and LCL) and evaluatingthem using the following goodness of fit statistics adjustedcoefficient of determination (Adj1198772) standard deviation ofthe residuals (119878

119910sdot119909) and CV of the residuals mean relative

standard error (MRSE) mean residual (MR) and graphicalanalysis of the residuals The computation and interpretationof these fit statistics were previously described by Goicoa etal [5] Gadow and Hui [38] Meyer [39] Magalhaes [40] andRuiz-Peinado et al [41]The best models are those with high-est Adj1198772 smallest 119878

119910sdot119909 and CV of the residuals MRSE and

MRandwith the residual plots showing noheteroscedasticityno dependencies or systematic discrepancies

In addition to the goodness of fit statistics describedabove the methods of enforcing additivity were comparedusing percent standard error of the expected value andpercent standard error of the predicted value as computedin Table 4 The smaller the percent standard error of theexpected and percent standard error of the predicted valuesis the better the model is in predicting the biomass

SUR and NSURmethods were used instead of for exam-ple simply summing the best component biomass models(ie Harmonization procedure [42]) because in the lattercase the total biomass is not modelled and therefore its fit


Table 5 Regression coefficients and goodness of fit statistics for the best linear and nonlinear models in (3) and (4) respectively

Treecomponent

Weightfunction 119887

0(plusmnSE) 119887

1(plusmnSE) 119887

2(plusmnSE) Adj1198772

()119878119910sdot119909

(kg)CV()

MRSE(kg)

MR(kg)

Linear modelsRoots 1119863

2119867 02522 (plusmn06334) 00097 (plusmn00002) 9494 959 2010 01520 minus205119864 minus 14

Stem wood 11198632119867 06616 (plusmn11451) 00251 (plusmn00004) 9749 1966 1584 00255 minus796119864 minus 16

Stem bark 11198632119867 01895 (plusmn03503) 00028 (plusmn00001) 8424 497 3497 03397 minus196119864 minus 16

Crown 11198632119867 minus19106 (plusmn15216) 00984 (plusmn00044) 8424 2706 4634 10292 minus243119864 minus 01

Total tree 11198632119867 14066 (plusmn21984) 00494 (plusmn00008) 9761 3492 1429 00247 minus124119864 minus 15

Nonlinear modelsRoots 1119863

2119867 00091 (plusmn00024) 10074 (plusmn00841) 9494 1040 2179 01480 190119864 minus 05

Stem wood 11198632119867 00197 (plusmn00063) 18210 (plusmn00567) 13081 (plusmn01559) 9771 1883 1518 00272 minus340119864 minus 04

Stem bark 11198632119867 00022 (plusmn00019) 17451 (plusmn01564) 14084 (plusmn04355) 8484 570 4011 03770 minus204119864 minus 03

Crown 11198632119867 00350 (plusmn00137) 21318 (plusmn01385) 05290 (plusmn01482) 8442 2689 4605 05396 minus259119864 minus 01

Total tree 11198632119867 00533 (plusmn00093) 09920 (plusmn00196) 9760 3868 1583 01192 110119864 minus 05

SE = standard error ldquordquo = significant at 120572 ge 5 ldquo rdquo = not significant at any probability level

statistics are unknown and because the sum of tree compo-nent models with the best fits does not guarantee good fit inthe totalmodel andmight produce biased estimates for wholetree biomass [6] and further because SUR andNSUR unlikethe CON method take into account the contemporaneouscorrelation among residuals of the component equations [413 14 24]

Nevertheless the standard deviation and CV of the resid-uals for the harmonization approach (HAR) were comparedwith those obtained for SUR and NSUR approaches Since inHAR procedure the total tree biomass is obtained simply bysumming the best componentmodels the standard deviationof the residuals can be computed using the variance of a sum(6) [4 13] Consider

119878119910sdot119909(Total) = radic

119888

sum

119894=1

1198782

119910sdot119909(119894)+ 2sumsum119878

119894119895 (6)

where 119878119910sdot119909(Total) and 119878119910sdot119909(119894) are the standard deviation of the

residuals of the total tree biomass model and of the 119894th treecomponent biomassmodel and 119878

119894119895is the covariance of 119894th and

119895th tree component biomass modelsThe CV of the residuals is therefore computed as

CV(Total) =

119878119910sdot119909(Total)

119884totaltimes 100 (7)

where 119884total is the average total tree biomass (per tree)

3 Results

31 Independent Tree Component and Total Tree Models Thefit statistics and the coefficient of regression for the best treecomponent and total tree models are given in Table 5 forlinear and nonlinear models

All linear and nonlinear regression equations yielded sat-isfactory fit statisticsThe linearmodels presented an adjusted1198772 varying from 8424 for stem bark and crown biomass

regressions to 9761 for total tree biomass regression theprecision as measured by the coefficient of variation (CV)of the residuals varied from 1429 for total tree biomassregression to 4634 for crown biomass regression On theother hand the adjusted1198772 for nonlinearmodels varied from8442 for crown biomass regression to 9760 for total treebiomass regression and the CV of the residuals varied from1518 to 4605 For either linear or nonlinear models thebiases as measured by the mean residual (MR) were foundto be statistically not significant using Studentrsquos t-test andrelatively poor fit statistics were found for stem bark andcrown biomass regressions

32 Forcing Additivity In themodels in (1) themost frequentbest linear model form is = 119887

0+ 11988711198632119867 which was found

to be the best for the root system stem wood stem barkand total tree biomasses This model form was also rankedas the second model form for crown biomass Therefore toenforce additivity using the CON approach this model formwas generalized for all tree components and for total treebiomasses as can be seen from (3) Tables 6 and 7 illustratethe regression coefficients and the goodness of fit statisticsrespectively for the CON method presented in (3) the SURmethod in (4) and the NSUR method in (5)

321The CONMethod The results of the CONmethodwerethe same as for equation-by-equationWLS in Table 5 exceptthat the model for crown biomass was replaced in order tohave the same regressors as the remaining tree componentsBetter performances were found for total tree belowgroundand stem wood biomass regressions

Thegraphs of the residuals against predicted values for theCONmethod are presented in Figure 2 and did not show anyparticular trend or heteroscedasticity The cluster of pointswas contained in a horizontal band showing no particulartrend with the residuals almost evenly distributed underand over the axis of abscissas meaning that there were notobvious model defects


Table 6 Coefficients of regression for CON SUR and NSUR methods

Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887

2(plusmnSE) 119887

3(plusmnSE) 119887

4(plusmnSE)

CONmethodRoots 1119863

2119867 02522 (plusmn06334) 00097 (plusmn00002)



Crown 11198632119867 03033 (plusmn15640) 00118 (plusmn00006)

Total tree 11198632119867 14066 (plusmn21984) 00494 (plusmn00008)

SUR methodRoots 1119863

2119867 16513 (plusmn23498) 01016 (plusmn00040) minus04056 (plusmn02584)

Stem wood 11198632119867 minus38911 (plusmn09553) 02106 (plusmn00047)



Total tree 11198632119867 minus40843 (plusmn31723) 03122 (plusmn00068) 00014 (plusmn00001) 01114 (plusmn00044) minus04056 (plusmn02584)

NSUR methodRoots 1119863

2119867 00075 (plusmn00022) 10137 (plusmn00326)

Stem wood 11198632119867 00131 (plusmn00040) 17962 (plusmn00549) 14113 (plusmn01470)

Stem bark 11198632119867 00001 (plusmn00011) 16545 (plusmn01942) 17332 (plusmn05460)

Crown 11198632119867 00407 (plusmn00159) 22302 (plusmn01343) 03146 (plusmn01214)

Total tree 11198632119867


Table 7 Fit statistics for CON SUR and NSUR methods

Treecomponent

Weightfunction Adj1198772 () 119878

119910sdot119909(kg) CV () MRSE (kg) MR (kg)

1198941198942

SUR 2

NSUR


2119867 9494 959 2010 01520 minus205119864 minus 14 mdash

Stem wood 11198632119867 9749 1966 1584 00255 minus796119864 minus 16 mdash

Stem bark 11198632119867 8424 497 3497 03397 minus196119864 minus 16 mdash mdash mdash

Crown 11198632119867 8216 2511 4301 15596 171119864 minus 15 mdash

Total tree 11198632119867 9761 3492 1429 00247 minus124119864 minus 15 mdash


2119867 8244 2206 4624 01378 01769 00581

Stem wood 11198632119867 7247 6059 4883 01732 06599 05943

Stem bark 11198632119867 5284 1056 7438 02403 00930 00157 09906 mdash

Crown 11198632119867 8196 2722 4662 14330 minus01188 01053

Total tree 11198632119867 8688 9667 3956 00791 08109 91562


2119867 9276 1284 2692 01168 00805 00244

Stem wood 11198632119867 9227 3566 2874 00440 03116 01718

Stem bark 11198632119867 7812 685 4825 02084 00423 00072 mdash 47801

Crown 11198632119867 8527 2641 4523 08348 minus00049 00859

Total tree 11198632119867 6776 5332 2182 00321 04296 67590


322 SUR Method As can be verified from Table 7 theadjusted 1198772 varied from 5284 for stem bark to 8688 fortotal tree biomass regression and the CVs of the residualsvaried from 3956 for total tree biomass regression to

7438 for stem bark All tree components and total treemodels were found to be biased and all of these modelsunderestimated the biomass except for the crown biomasswhich was overestimated as was observed from the mean


000

1000

2000

3000

4000

0 50 100 150 200

Resid

uals

()

Predicted belowground biomass (kg)

minus5000

minus4000

minus3000

minus2000

minus1000

(a)

000

1000

2000

3000

4000

0 100 200 300 400 500

Resid

uals

()

Predicted stem wood biomass (kg)

minus4000

minus3000

minus2000

minus1000

(b)

0 10 20 30 40 50Predicted stem bark biomass (kg)

000

2000

4000

6000

8000

Resid

uals

()

minus8000

minus6000

minus4000

minus2000

(c)

000

2000

4000

6000

8000

0 50 100 150 200Re

sidua

ls (

)Predicted crown biomass (kg)

minus8000

minus6000

minus4000

minus2000

(d)

000

1000

2000

3000

0 200 400 600 800

Resid

uals

()

Predicted total tree biomass (kg)

minus3000

minus2000

minus1000

(e)

Figure 2 Residuals against predicted biomass for the CONmethod (a) belowground (b) stem wood (c) stem bark (d) crown and (e) totaltree biomass

residual (MR) Using Studentrsquos t-test these biases (MRs) werefound to be statistically significant (statistically different fromzero)

The biases model defects (under andor overestimationheteroscedasticity) and patterns that indicated systematicdiscrepancies are illustrated by the graph of the residualsin Figure 3 Analyses of the residuals for SUR did notreveal heteroscedasticity but showed that the residuals weremostly agglomerated over the axis of abscissas meaning thatthe designed models predicted biomass values smaller thanthe observed ones underestimating the biomass (producingpositive residuals) This happened to all tree componentsexcept for the crown biomass

323 NSUR Method Component models (Tables 6 and 7)showed an adjusted 1198772 varying from 7812 for stem barkto 9276 for roots The lowest adjusted 1198772 was found forthe total tree model (6776) The CVs of the residualsvaried from 2182 for total tree to 4825 for the stembark model All tree components (except the crown) and thetotal tree models were biased underestimating the biomasssignificantly as shown by the observation that the MRs weresignificantly different from zero

Overall the distribution of the residuals (Figure 4) wassatisfactory Minor defects were found for crown and totaltree models


000

2000

4000

6000

8000

0 20 40 60 80 100 120

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(a)

000

2000

4000

6000

8000

0 50 100 150 200 250

Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(b)

000

2000

4000

6000

8000

10000

00 50 100 150 200 250Resid

uals

()

Predicted stem bark biomass (kg)

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()

Predicted crown biomass (kg)

minus10000

minus15000

minus5000

(d)

000

2000

4000

6000

0 100 200 300 400 500 600

Resid

uals

()


minus6000

minus4000

minus2000

(e)

Figure 3 Residuals against the predicted biomass for the SUR method (a) belowground (b) stem wood (c) stem bark (d) crown and (e)total tree biomass

Comparing the different methods based on the relativestandard errors of the expected and predicted values fortotal tree biomass computed from 11 randomly selectedtrees from different diameter classes (Table 8) we found thatthe conventional method had the smallest average standarderrors of the expected and predicted total tree biomass values(202 and 220 resp) followed by the NSUR method(352 and 368 resp) and lastly the SUR method (772and 775 resp) These data indicated that the CONmethodyielded narrower confidence and prediction intervals thanthe NSUR and SUR methods

4 Discussion

41 Independent Tree Component and Total TreeModels Lin-ear and nonlinear models were fitted for tree component andtotal tree biomass estimationThe difference between the per-formance of the selected linear and nonlinear tree componentmodels is negligible However Salis et al [43] Ter-Mikaelianand Korzukhin [44] and Schroeder et al [45] found nonlin-ear models to perform better than the linear ones

The crown models for both linear and nonlinear modelswere found to be less accurate and precise than the other tree


000

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140Resid

uals

()


minus3000

minus4000

minus2000

minus1000

(a)

1000

2000

3000

4000

0000

50 100 150 200 250 300 350

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(b)

0002000400060008000

10000

0 5 10 15 20 25 30 35 40

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800Resid

uals

()


minus3000

minus2000

minus1000

(e)

Figure 4 Residuals against predicted biomass for the NSURmethod (a) belowground (b) stemwood (c) stem bark (d) crown and (e) totaltree biomass

componentmodels as evaluated by its adjusted1198772 andCVs ofthe residuals suggesting more variability According to Parde[46] as cited by Carvalho and Parresol [14] this is becauseof the variability of the internal crown structure number ofbranches and variation in wood density along the branches

42 Additivity Based on all of the results and analyses theCON method was significantly superior to the SUR andNSUR methods and showed the best fit statistics for everytree component and total tree biomass models includingthe largest adjusted 1198772 smallest CV of the residuals andno significant model bias or defects However althoughthe CON method was found to be statistically superior itshould be noted that it holds only under the assumption

of independence among components [4] implying that theresiduals are interrelated therefore not taking into accountcontemporaneous correlations

Among the methods that consider contemporaneouscorrelations (ie SUR and NSUR) NSUR appeared superiorto SUR For all tree components NSUR was superior to SURwith the higher adjusted 1198772 smaller CV of the residuals andless bias However the total tree model of the SUR methodpresented a higher adjusted 1198772 when compared to the totaltree model of the NSUR method Figure 5 shows that theSUR method described the data quite poorly whereas theCON and NSUR methods described the data satisfactorilyeven for the total tree model for which the SUR methodhad the higher adjusted 1198772 value than the NSUR method


Table 8 Relative standard errors () of the expected and predicted total tree biomass values for 11 randomly selected trees

119863 119867 CH LCL CON SUR NSUR119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660

Average 20167 21930 77198 77489 35182 36801119878(119864(1199100)) = relative standard error of the expected value 119878(1199100119894 minus 119910) = relative standard error of the predicted value

Table 9 119905-test for the restriction imposed for weighted SUR

Restriction DF Parameter estimate Standard error 119905 value Pr gt |119905|11988750= 11988710+ 11988720+ 11988730+ 11988740

minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712

minus1 47892 14875 322 00010Note the restrictions are as stated in (4)

The predicted regression lines in Figure 5 were obtained from11 randomly selected trees from different diameter classes (2trees per diameter class except the last where only 1 tree wasselected due to fewer representative trees) therefore the linesare function of changing all variables (refer to Table 8) henceexhibiting waves since other variables (119867 CH and LCL) didnot necessarily increase as DBH increased

As shown in Figure 5 the regression lines for the CONand NSUR methods followed the same trend and the CONmethod described the data slightly better than the NSURmethod Additionally for all components the SUR regressionline was the poorest fit especially for belowground stemwood stem bark and total tree biomasses

As shown inTable 7 the variance of theNSUR systemwasalmost five times larger than that of the SUR system howeverthe covariance errors for all tree components were almost twotimes smaller for the NSUR method this last observationmay explain the better fit of the NSUR method as all of thecomponents in the NSUR method had larger 1198772 values andsmaller CVs of the residuals than those in the SUR method

Several authors including Parresol [4 13] Carvalho andParresol [14] Goicoa et al [5] Carvalho [37] and Navar-Chaidez et al [42] have compared different methods ofenforcing additivity All of these authors have concluded thateither SUR or NSUR achieves more efficient estimates andshould be the choice for additivity However Parresol [4]suggests that the constraint of additivity (restriction of theparameters) may compromise the efficiency of the results

a conclusion supported by SAS Institute Inc [33] which statesthat restrictions should be consistent and not redundant thatis the data must be consistent with the restriction In factthe lower efficiency and precision of the SUR and NSURestimates when compared to the CONmethod are associatedwith the imposed restriction as t-test results based on allthe restrictions imposed on SUR and NSUR were highlysignificant indicating that the data were not consistent withthe restriction and that the models did not fit as well with therestriction imposed For greater details please see Tables 9and 10 which are SAS outputs that test the significance of therestrictions imposed for weighted SUR and weighted NSURrespectively

Carvalho [37] compared methods of enforcing additivityand found that the bias (MR) for stem wood was slightlylarger when the models were fitted simultaneously usingSUR than when tree components were fitted separately usingordinary least squares (OLS) even though other fit statisticshad improved with SUR Similar findings were observed byGoicoa et al [5] who found that the SURmethod was highlybiased as it exhibited large MR and mean relative standarderror (MRSE) values

Parresol [4 13] Carvalho and Parresol [14] and Carvalho[37] found that multivariate procedures (SUR andor NSUR)produce more reliable estimates than when equations areestimated independently (eg the CONmethod or indepen-dent tree component models) However Repola [47] foundno significant improvements in parameter estimates using


0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR

NSURObserved belowground biomass

(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)

Observed stem wood biomass CONSUR

NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)

Observed stem bark biomass CONSUR

NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)

Observed crown biomass CONSUR

NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)

Observed total tree biomass CONSUR

NSUR

(e)

Figure 5 Observed biomass versus DBH values and regression lines obtained from the different methods of achieving additivity for (a)belowground (b) stem wood (c) stem bark (d) crown and (e) total tree biomass


Table 10 t-test for the restriction imposed for weighted NSUR

Restriction Parameterestimate

Standarderror 119905 value Pr gt |119905|

Res1 minus316270 35620 minus888 lt00001Res2 minus21046 2376 minus886 lt00001Res3 minus439279 48980 minus897 lt00001Res4 minus17830 1999 minus892 lt00001Res5 minus15095 1678 minus900 lt00001Res6 minus681146 73260 minus930 lt00001Res7 minus2027 219 minus925 lt00001Res8 minus1720 185 minus931 lt00001Res9 minus87764 9486 minus925 lt00001Res10 minus11199 1220 minus918 lt00001Res11 minus8474 880 minus963 lt00001Note res1 to res11 are the restrictions imposed to each of the 11 regressioncoefficients in the total tree model as stated in (5)

SUR when compared to the case where the models are fittedindependently

Due to the large bias found using the SUR method thismethod cannot be used for biomass estimation of any treecomponent However because the bias is far smaller thanthat of the SUR method the NSUR method can be usedfor biomass estimation as long as the bias is consideredMoreover while the NSUR method is not superior to theCON method in terms of bias it does have the advantageof considering contemporaneous correlation which theCONmethod does not

The CV of the residuals for total tree biomass modelobtained using the HAR procedure for the linear and nonlin-earmodels was 724 and 69 respectively 83 and 216 largerthan the CV for total tree model obtained using the SUR andNSUR procedures respectively This shows that in this casethe model for total biomass obtained using SUR or NSURprocedure provides more precise results than what would beobtained by summing up the individual component modelsto the total (HAR procedure)

43 Extrapolation The models fitted in this research (sepa-rately or simultaneously) are based on a dataset of 93 treeswith diameters varying from 5 to 32 cmA johnsonii trees canreach diameters at breast height (DBHs) larger than 35 cmIn a forest inventory of A johnsonii tree with a minimumDBH of 10 cm Magalhaes and Soto [48] (unpublished data)found only 13 trees per ha with DBHs larger than or equal to30 cm corresponding to only 5 of trees per ha In this studyusing 23 plots randomly distributed in the study area and aminimum DBH of 5 cm we found only 19 trees per ha withdiameters larger than or equal to 325 cm corresponding to154 of the total number of trees per haThis implied that noserious bias would be added when extrapolating the models(independent tree component or NSUR models) outside thediameter range used to fit themodels since very few treeswerefound outside the diameter range

Themodels can also be safely applicable and valid over thewhole range of areas where A johnsonii occurs and outsidethe study areaThis is true because the study area covered theentire range of soil and climate variations where A johnsoniioccurs (despite the apparent lack of large variations) Forexample besides the Chibuto Mandlakazi Panda Fun-halouro and Mabote districts that comprised the study areaMecrusse (A johnsonii stands) is also found in MabalaneMassangena and Chicualacuala districts However in theselatter districts the soils were nearly identical to those ofthe study area composed mainly of Ferralic Arenosols [1622] Similarities were also found with regard to climate andhydrology especially with regard to rain shortage [17ndash21]

44 Effect of theMeasurement Procedures on the Estimates Inthis study wood density was obtained by dividing oven dryweight (at 105∘C) of the discs (with and without bark) by therelevant saturated wood volume [27 30] (air not included)It is noteworthy to mention that different definitions of theweight and volume of the discs would potentially influencethe estimates of density and therefore biomass For exampleHusch et al [28] define density as the ratio of oven dry weightand green volume (air included) Compared to the definitionadopted by us such a definition would potentially lead tolarge values of wood density and consequentlywood biomassas saturated volume is the maximum volume [49] and isexpected to be larger than green volume

Moura et al [49] found no significant differences betweenthose densities as according to these authors the densitiesmust be quite the same because volume is not expectedto vary above the fibre saturation point (FSP) FSP of awood is here defined as the maximum possible amount ofwater that the composite polymers of the cell wall can holdat a particular temperature and pressure [50] excludingtherefore free and adsorbed water Differences in wooddensity and biomass estimates could also be found if the discswere dried to different moisture content (eg 12) or if adifferent drying temperature was used (eg 65∘C)

Stem was defined as the length from the top of the stumpto the height corresponding to 25 cm diameter Differencesamong stem definitions (eg different stump height ordifferent minimum top diameter stump considered as part ofthe stem) would affect the biomass estimates especially stemand root biomasses Different estimates of root biomass couldalso be found if the root system was partially removed asperformed by many authors (eg [41 51ndash54]) if the depthsof excavation were predefined [41 51 55] if fine roots wereexcluded [56 57] and if root sampling procedures wereapplied for example where only a number of roots from eachroot system are fully excavated and then the informationfrom the excavated roots is used to estimate biomass for theroots not excavated [58ndash60]

5 Conclusions

This study showed that CON method was found to beunbiased and to fit the tree component and total tree biomasswell however the CON method had the disadvantage of not


considering contemporaneous correlations Amongmethodsthat consider contemporaneous correlations NSUR was farsuperior to SUR and fit the biomass reasonably well howeverboth methods were significantly biased The CON methodcan be used safely as long as its limitation is consideredThe NSUR method can also be used as long as the bias isaccepted and taken into account Moreover we recommendthat the SUR method should not be used due to its bias andpoor description of biomass data Since the data sets usedto build the models (both independent and simultaneous)representedmany variations (all diameters soils and climaticranges) the selected models can be used for extrapolation

Appendix

See Figure 1 and Tables 2 and 3The Table 3 shows the results of SUR using the system of

the best linear model forms However as 3 of the 5 equationsin the system use the same independent variables the SURis not effective it has lower adjusted 1198772 sometimes negativelarger CV of the residuals larger system variance (2SUR) andlarger component covariance errors (

119894119894) when compared to

the results in Tables 6 and 7 The most jeopardized equationsare those sharing the same independent variables

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This study was funded by the Swedish International Devel-opment Cooperation Agency (SIDA) Thanks are extendedto Professor Almeida Sitoe for his advices during the prepa-ration of the field work and to the field and laboratoryteam involved in felling excavation and fresh- and dry-weighing of trees and tree samples Albino Americo MabjaiaSalomao dos Anjos Baptista Amelia Saraiva MonguelaJoao Paulino Alzido Macamo Jaime Bule Adolfo ZunguzeViriato Chiconele Murrombe Paulo Goba Dinısio JulioGerente Guarinare Sa Nogueira Lisboa Francisco UssivaneNkassa Amade Candida Zita and Jose Alfredo AmanzeThe authors would also like to thank the members of localcommunities community leaders and Madeiraarte ForestConcession for the unconditional help Acknowledges arealso due to two anonymous reviewers whose insightfulcomments and suggestions have improved considerably thispaper

References

[1] G A Cardoso Madeiras de Mocambique Androstachys john-sonii Servicos deAgricultura e Servicos deVeterinariaMaputoMozambique 1963

[2] P Leadley H M Pereira R Alkemade et al ldquoBiodiversityscenarios projections of 21st century change in biodiversity andassociated ecosystem servicesrdquo Technical Series 50 Secretariat

of the Convention on Biological Diversity Montreal Canada2010

[3] T Brandeis D Matthew L Royer and B Parresol ldquoAllometricequations for predicting Puerto Rican dry forest biomass andvolumerdquo in Proceedings of the 18th Annual Forest Inventory andAnalysis Symposium pp 197ndash202 2006

[4] B R Parresol ldquoAssessing tree and stand biomass a review withexamples and critical comparisonsrdquo Forest Science vol 45 no4 pp 573ndash593 1999

[5] T Goicoa A F Militino and M D Ugarte ldquoModelling above-ground tree biomass while achieving the additivity propertyrdquoEnvironmental and Ecological Statistics vol 18 no 2 pp 367ndash384 2011

[6] K Repola Modelling tree biomasses in Finland [PhD thesis]University of Helsinki Helsinki Finland 2013

[7] C M Litton M G Ryan D B Tinker and D H KnightldquoBelowground and aboveground biomass in young postfirelodgepole pine forests of contrasting tree densityrdquo CanadianJournal of Forest Research vol 33 no 2 pp 351ndash363 2003

[8] A Kozak ldquoMethods for ensuring additivity of biomass compo-nents by regression analysisrdquoThe Forestry Chronicle vol 46 no5 pp 402ndash405 1970

[9] T Cunia ldquoOn tree biomass tables and regression some statisti-cal commentsrdquo in Proceedings of the Forest Resource InventoryWorkshop W E Frawer Ed pp 629ndash642 Colorado StateUniversity Fort Collins Colo USA July 1979

[10] T Cunia and R D Briggs ldquoForcing additivity of biomass tablessome empirical resultsrdquo Canadian Journal of Forest Researchvol 14 no 3 pp 376ndash385 1984

[11] T Cunia and R D Briggs ldquoForcing additivity of biomass tablesuse of the generalized least squares methodrdquo Canadian Journalof Forest Research vol 15 no 1 pp 23ndash28 1985

[12] M W Jacobs and T Cunia ldquoUse of dummy variables toharmonize tree biomass tablesrdquo Canadian Journal of ForestResearch vol 10 no 4 pp 483ndash490 1980

[13] B R Parresol ldquoAdditivity of nonlinear biomass equationsrdquoCanadian Journal of Forest Research vol 31 no 5 pp 865ndash8782001

[14] J P Carvalho and B R Parresol ldquoAdditivity in tree biomasscomponents of Pyrenean oak (Quercus pyrenaicaWilld)rdquoForestEcology and Management vol 179 no 1ndash3 pp 269ndash276 2003

[15] J Mantilla and R TimaneOrientacao para maneio de mecrusseSymfoDesign Maputo Mozambique 2005

[16] DINAGECA Mapa Digital de Uso e Cobertura de TerraCENACARTA Maputo Mozambique 1990

[17] MAE Perfil do Distrito de Chibuto Provıncia de Gaza MAEMaputo Mozambique 2005

[18] MAE Perfil do Distrito de Mandhlakaze Provıncia de GazaMAE Maputo Mozambique 2005

[19] MAE Perfil do Distrito de Panda Provıncia de InhambaneMAE Maputo Mozambique 2005

[20] MAE Perfil do Distrito de Funhalouro Provıncia de InhambaneMAE Maputo Mozambique 2005

[21] MAE Perfil do distrito de Mabote provincia de InhambaneMAE Maputo Mocambique 2005

[22] FAO FAOMap of World Soil Resources FAO Rome Italy 2003[23] M-C Lambert C-H Ung and F Raulier ldquoCanadian national

tree aboveground biomass equationsrdquo Canadian Journal ofForest Research vol 35 no 8 pp 1996ndash2018 2005


[24] B R Parresol and C E Thomas ldquoEconometric modeling ofsweetgum stem biomass using the IML and SYSLIN proce-duresrdquo in Proceedings of the 16th Annual SAS Userrsquos GroupInternational Conference pp 694ndash699 SAS Institute Cary NCUSA 1991

[25] G W Snedecor and W G Cochran Statistical Methods IowaState University Press Ames Iowa USA 8th edition 1989

[26] R D Yanai J J Battles A D Richardson C A Blodgett D MWood and E B Rastetter ldquoEstimating uncertainty in ecosystembudget calculationsrdquo Ecosystems vol 13 no 2 pp 239ndash2482010

[27] I A Gier Forest Mensuration (Fundamentals) InternationalInstitute for Aerospace Survey and Earth Sciences (ITC)Enschede The Netherlands 1992

[28] B Husch TW Beers and J A Kershaw Jr Forest MensurationJohn Wiley amp Sons New York NY USA 4th edition 2003

[29] M A M Brasil R A A Veiga and J L Timoni ldquoErros nadeterminacao da densidade basica da madeirardquo CERNE vol 1no 1 pp 55ndash57 1994

[30] J Bunster Commercial Timbers of Mozambique TechnologicalCatalogue Traforest Maputo Mozambique 2006

[31] T Seifert and S Seifert ldquoModelling and simulation of treebiomassrdquo inBioenergy fromWood Sustainable Production in theTropics T Seifert Ed vol 26 ofManaging Forest Ecosystems pp43ndash65 Springer Amsterdam The Netherlands 2014

[32] R Core Team R A Language and Environment for StatisticalComputing R Foundation for Statistical Computing ViennaAustria 2013

[33] SAS Institute SASETS Userrsquos Guide Version 8 SAS InstituteCary NC USA 1999

[34] V K Srivastava and D E A Giles Seemingly UnrelatedRegression Equations Models Estimation and Inference MarcelDekker Inc New York NY USA 1987

[35] W H Greene Econometric Analysis Macmillan New York NYUSA 2nd edition 1989

[36] D Bhattacharya ldquoSeemingly unrelated regressions with identi-cal regressors a noterdquo Economics Letters vol 85 no 2 pp 247ndash255 2004

[37] J P Carvalho ldquoUso da propriedade da aditividade de compo-nentes de biomassa individual deQuercus pyrenaicaWilld comrescurso a um sistema de equacoes nao linearrdquo Silva Lusitanavol 11 pp 141ndash152 2003

[38] K V Gadow and G Y Hui Modelling Forest DevelopmentKluwer Academic Publishers Dordrecht The Netherlands1999

[39] H A Meyer A Correction for a Systematic Errors Occurring inthe Application of the Logarithmic Volume Equation ForestrySchool Research State College Pa USA 1941

[40] T M Magalhaes Calibration of commercial volume and formfactor tables for Androstachys johnsonii for Madeiraarte conces-sion in Changanine-Memo villages [MS thesis] University ofCopenhagen Copenhagen Denmark 2008

[41] R Ruiz-Peinado M del Rio and G Montero ldquoNew modelsfor estimating the carbon sink capacity of Spanish softwoodspeciesrdquo Forest Systems vol 20 no 1 pp 176ndash188 2011

[42] J J Navar-Chaidez N G Barrientos J J G Luna V Daleand B Parresol ldquoAdditive biomass equations for pine species offorest plantations of Durango Mexicordquo Madera y Bosques vol10 no 2 pp 17ndash28 2004

[43] S M Salis M A Assis P P Mattos and A C S PiaoldquoEstimating the aboveground biomass and wood volume ofsavanna woodlands in Brazilrsquos Pantanal wetlands based onallometric correlationsrdquo Forest Ecology and Management vol228 no 1ndash3 pp 61ndash68 2006

[44] M T Ter-Mikaelian and M D Korzukhin ldquoBiomass equationsfor sixty-five North American tree speciesrdquo Forest Ecology andManagement vol 97 no 1 pp 1ndash24 1997

[45] P Schroeder S Brown J Mo R Birdsey and C CieszewskildquoBiomass estimation for temperate broadleaf forests of theUnited States using inventory datardquo Forest Science vol 43 no3 pp 424ndash434 1997

[46] J D Parde ldquoForest biomassrdquo Forest Abstracts vol 41 pp 343ndash362 1980

[47] J Repola ldquoBiomass equations for birch in Finlandrdquo SilvaFennica vol 42 no 4 pp 605ndash624 2008

[48] T M Magalhaes and S J Soto Relatorio de Inventario Florestalda Concessao Florestal de Madeiraarte Bases para a elaboracaodo plano de maneio de conservacao dos recursos naturaisDepartamento de Engenharia Florestal (DEF) UniversidadeEduardo Mondlane (UEM) Maputo Mozambique 2005

[49] S Moura D Abella and O Anjos ldquoEvaluation of wood basicdensity as an indirect measurement of the volume of wood rawmaterialrdquo in Proceedings of the Wood Science and Engineering intheThirdMillennium (ICWSE rsquo07) pp 72ndash78 Brasov RomaniaJune 2007

[50] L A Simpson and A F M Barton ldquoDetermination of thefibre saturation point in whole wood using differential scanningcalorimetryrdquo Wood Science and Technology vol 25 no 4 pp301ndash308 1991

[51] C R Sanquetta A P D Corte and F Da Silva ldquoBiomassexpansion factor and root-to-shoot ratio for Pinus in BrazilrdquoCarbon Balance and Management vol 6 article 6 pp 1ndash8 2011

[52] P E Levy S E Hale and B C Nicoll ldquoBiomass expansionfactors and root shoot ratios for coniferous tree species inGreatBritainrdquo Forestry vol 77 no 5 pp 421ndash430 2004

[53] N Soethe J Lehmann and C Engels ldquoRoot tapering betweenbranching points should be included in fractal root systemanalysisrdquo Ecological Modelling vol 207 no 2ndash4 pp 363ndash3662007

[54] T Kalliokoski P Nygren and R Sievanen ldquoCoarse root archi-tecture of three boreal tree species growing in mixed standsrdquoSilva Fennica vol 42 no 2 pp 189ndash210 2008

[55] K I Paul S H Roxburgh J R England et al ldquoRoot biomassof carbon plantings in agricultural landscapes of southern Aus-tralia development and testing of allometricsrdquo Forest Ecologyand Management vol 318 pp 216ndash227 2014

[56] C M Ryan M Williams and J Grace ldquoAbove- and below-ground carbon stocks in a miombo woodland landscape ofmozambiquerdquo Biotropica vol 43 no 4 pp 423ndash432 2011

[57] A Bolte T RahmannM Kuhr P Pogoda DMurach and K VGadow ldquoRelationships between tree dimension and coarse rootbiomass in mixed stands of European beech (Fagus sylvatica L)and Norway spruce (Picea abies [L] Karst)rdquo Plant and Soil vol264 no 1-2 pp 1ndash11 2004

[58] W A Mugasha T Eid O M Bollandsas et al ldquoAllometricmodels for prediction of above- and belowground biomass oftrees in themiombowoodlands of Tanzaniardquo Forest Ecology andManagement vol 310 pp 87ndash101 2013


[59] S Kuyah J Dietz C Muthuri et al ldquoAllometric equations forestimating biomass in agricultural landscapes II BelowgroundbiomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[60] K Niiyama T Kajimoto Y Matsuura et al ldquoEstimation of rootbiomass based on excavation of individual root systems in aprimary dipterocarp forest in Pasoh Forest Reserve PeninsularMalaysiardquo Journal of Tropical Ecology vol 26 no 3 pp 271ndash2842010

Submit your manuscripts athttpwwwhindawicom

Forestry ResearchInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Environmental and Public Health

Journal of



EcosystemsJournal of


MeteorologyAdvances in

EcologyInternational Journal of


Marine BiologyJournal of


Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Advances in


Environmental Chemistry

Atmospheric SciencesInternational Journal of



Waste ManagementJournal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics


Geological ResearchJournal of

EarthquakesJournal of


BiodiversityInternational Journal of


ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


ClimatologyJournal of


Table 1 Summary statistics for the independent and dependent variables

Variable Minimum Q025 Median Average Q075 Maximum SD CV ()DBH (cm) 500 1100 1750 1759 2400 3200 751 4272Total tree height119867 (m) 569 1121 1277 1232 1390 1600 214 1735Crown height CH (m) 070 374 516 505 615 992 201 3986Live crown length LCL (m) 110 550 705 727 890 1350 247 3405Belowground biomass (kg) 255 1166 3604 4773 7349 16210 4121 8633Stem wood biomass (kg) 495 3051 10318 12407 19762 35735 9950 8020Stem bark biomass (kg) 068 352 1117 1420 2260 5580 1237 8714Crown biomass (kg) 304 1368 3736 5839 8044 21669 5908 10117Total tree biomass (kg) 1248 5990 20439 24439 36823 75257 20433 8361Q025 = first quartile Q075 = third quartile SD = standard deviation CV = coefficient of variation

(iv) the stump and root system are left in the forest allowingthe stump to either sprout (regrow) continuing the seques-tration process or decompose along with the roots releasingCO2and nutrients and (v) in some tree species belowground

biomass can account for more than one-third of the totalbiomass [7] Hence it is critical to estimate the biomass ofall tree components as well as the total tree biomass in orderto assess the global carbon balance

However the biomass estimates of the considered treecomponents often do not sum to the estimate of the totaltree biomass and a desired and logical feature of the treecomponent regression equations is that the predictions of thecomponents sum to the prediction for the total tree Thisfeature is called additivity Various authors such as Goicoa etal [5] Kozak [8] Cunia [9] Cunia and Briggs [10 11] Jacobsand Cunia [12] Parresol [4 13] and Carvalho and Parresol[14] have proposed andor discussed various methods toensure the property of additivity

The objective of this study was to fit independent lin-ear and nonlinear tree component and total tree biomassmodels and compare three methods of enforcing the prop-erty of additivity (the conventional (CON) method seem-ingly unrelated regression (SUR) with parameter restrictionand nonlinear seemingly unrelated regression (NSUR) withparameter restriction) for A johnsonii tree species

TheCONmethod consists of using the same independentvariables for all tree component models and for total treemodel and the same weights to enforce additivity [4] TheSUR and NSUR methods consist in first fitting and selectingthe best linear and nonlinear models respectively for eachtree component The total tree model is a function of theindependent variables used in each component model Thenall models including the total are fitted again simultaneouslyusing joint-generalized least squares under the restriction ofthe coefficients of regression which ensures the additivityproperty [4]

2 Materials and Methods21 Study Area Mecrusse is a forest type where the mainspecies many times the only one in the upper canopy is Ajohnsonii [15]

In Mozambique Mecrusse woodlands are mainly foundin Inhambane and Gaza provinces and in MassangenaChicualacuala Mabalane Chigubo Guija Mabote Fun-halouro Panda Mandlakazi and Chibuto districts Theeastern-most Mecrusse patches covering the last five dis-tricts were defined as the study area The study area had anextension of 4502828 ha [16] of which 226013 ha (5) wascovered by Mecrusse woodlands

The climate is dry and tropical throughout the study areaexcept in the west part of the Panda district and the southwestpart of the Mandlakazi district where the climate is humidand tropical [16ndash21] The climate has two seasons the warmor rainy season from October to March and the cool or dryseason fromMarch to September [17ndash21]

The mean annual temperature is generally greater than24∘C and the mean annual precipitation varies from 400to 950mm [16ndash21] According to FAO classification [22]the soils in the study area are mainly Ferralic Arenosolscovering more than 70 of the study area [16] ArenosolsUmbric Fluvisols and Stagnic soils are also predominant inthe northern-most part of the study area [16]

The study area is characterized by a shortage of waterresources as well as precipitation thus of the five districtsthat made up the study area only the districts of Chibutoand Mandlakazi have water resources [16ndash21] either fromprecipitation or from lakes and rivers

22 Data Acquisition A total of 93 trees (2 to 6 per plot)selected across all size classes (Table 1) were destructivelysampled within 23 circular plots randomly located in thestudy area Diameter at breast height (DBH) total tree height(119867) crown height (CH) and live crown length (LCL) weremeasured on the felled trees Trees were divided into thefollowing tree components (1) root system (2) stem wood(3) stem bark and (4) crown Tree components were sampledand the dry weights were estimated as follows

221 Root System The stump height was predefined as being20 cm for all trees and considered as part of the taprootas recommended by Parresol [13] and because in largerA johnsonii trees this stump height (20 cm) is affected by


(a) (b)

(c) (d)

(e) (f)


















Roots = 1198870 + 11988711198632119867

Stem-wood = 1198870 + 11988711198632119867

Stem-bark = 1198870 + 11988711198632119867

Crown = 1198870 + 11988711198632LCL025

Total-tree = 1198870 + 11988711198632119867

(1)

Roots = 1198870 (1198632119867)1198872

Stem-wood = 119887011986311988711198671198872

Stem-bark = 119887011986311988711198671198872

Crown = 11988701198631198871LCL1198872

Total-tree = 1198870 (1198632119867)1198872

(2)





1(plusmnSE) 119887

2(plusmnSE)









(kg) CV () MRSE (kg) MR (kg) 119894119894

2

SUR

Roots 11198632119867 5600 349040 731758 02750 03227 01503

Stem wood 11198632119867 2217 1166327 940069 05181 11685 17454

Stem bark 11198632119867 minus2922 181996 1281809 08488 01751 00432 10028

Crown 11198632119867 8150 285040 488144 14814 minus01298 01087

Total tree 11198632119867 6319 2495561 1021272 02332 15366 144049




Roots = 11988710 + 119887111198632119867

Stem-wood = 11988720 + 119887211198632119867

Stem-bark = 11988730 + 119887311198632119867

Crown = 11988740 + 119887411198632119867


= (11988710+ 11988720+ 11988730+ 11988740)

+ (11988711+ 11988721+ 11988731+ 11988741)1198632119867

= 11988750+ 119887511198632119867

(3)





21198632LCL025




Roots = 11988710 + 119887111198632+ 11988712119867

Stem-wood = 11988720 + 119887211198632

Stem-bark = 11988730 + 119887311198632119867

Crown = 11988740 + 119887411198632LCL025

Total = (11988710 + 11988720 + 11988730 + 11988740) + (11988711 + 11988721)1198632

+ 119887311198632119867 + 119887

411198632LCL025 + 119887

12119867

= 11988750+ 119887511198632+ 119887521198632119867 + 119887

531198632LCL025 + 119887

54119867

(4)







119899+(1199090minus 119909)2

SS119909

119878 (119864 (1199100)) =119878 (119864 (119910

0))

119910119894

times 100


119910sdot119909radic1 +1

119899+(1199090minus 119909)2

SS119909

119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100


2

119910119894+ 2

SUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100


2

119910119894+ 2

NSUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2





Roots = 11988710 (1198632119867)11988711

Stem-wood = 119887201198631198872111986711988722

Stem-bark = 119887301198631198873111986711988732

Crown = 1198874111986311988742LCL11988743

Total = 11988710 (1198632119867)11988711

+ 119887201198631198872111986711988722

+ 119887301198631198873111986711988732 + 1198874111986311988742LCL11988743

(5)













Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887


()119878119910sdot119909

(kg)CV()

MRSE(kg)

MR(kg)
















119878119910sdot119909(Total) = radic

119888

sum

119894=1

1198782

119910sdot119909(119894)+ 2sumsum119878

119894119895 (6)





CV(Total) =

119878119910sdot119909(Total)



3 Results





0+ 11988711198632119867 which was found






Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887

2(plusmnSE) 119887

3(plusmnSE) 119887

4(plusmnSE)


2119867 02522 (plusmn06334) 00097 (plusmn00002)












2119867 00075 (plusmn00022) 10137 (plusmn00326)




Total tree 11198632119867



Treecomponent



1198941198942

SUR 2

NSUR








2119867 8244 2206 4624 01378 01769 00581

Stem wood 11198632119867 7247 6059 4883 01732 06599 05943

Stem bark 11198632119867 5284 1056 7438 02403 00930 00157 09906 mdash

Crown 11198632119867 8196 2722 4662 14330 minus01188 01053

Total tree 11198632119867 8688 9667 3956 00791 08109 91562


2119867 9276 1284 2692 01168 00805 00244

Stem wood 11198632119867 9227 3566 2874 00440 03116 01718

Stem bark 11198632119867 7812 685 4825 02084 00423 00072 mdash 47801

Crown 11198632119867 8527 2641 4523 08348 minus00049 00859

Total tree 11198632119867 6776 5332 2182 00321 04296 67590





000

1000

2000

3000

4000

0 50 100 150 200

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(a)

000

1000

2000

3000

4000

0 100 200 300 400 500

Resid

uals

()


minus4000

minus3000

minus2000

minus1000

(b)


000

2000

4000

6000

8000

Resid

uals

()

minus8000

minus6000

minus4000

minus2000

(c)

000

2000

4000

6000

8000

0 50 100 150 200Re

sidua

ls (


minus8000

minus6000

minus4000

minus2000

(d)

000

1000

2000

3000

0 200 400 600 800

Resid

uals

()


minus3000

minus2000

minus1000

(e)







000

2000

4000

6000

8000

0 20 40 60 80 100 120

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(a)

000

2000

4000

6000

8000

0 50 100 150 200 250

Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(b)

000

2000

4000

6000

8000

10000

00 50 100 150 200 250Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

2000

4000

6000

0 100 200 300 400 500 600

Resid

uals

()


minus6000

minus4000

minus2000

(e)



4 Discussion




000

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140Resid

uals

()


minus3000

minus4000

minus2000

minus1000

(a)

1000

2000

3000

4000

0000

50 100 150 200 250 300 350

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(b)

0002000400060008000

10000

0 5 10 15 20 25 30 35 40

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800Resid

uals

()


minus3000

minus2000

minus1000

(e)









0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660




minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712










0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics















(a) (b)

(c) (d)

(e) (f)


















Roots = 1198870 + 11988711198632119867

Stem-wood = 1198870 + 11988711198632119867

Stem-bark = 1198870 + 11988711198632119867

Crown = 1198870 + 11988711198632LCL025

Total-tree = 1198870 + 11988711198632119867

(1)

Roots = 1198870 (1198632119867)1198872

Stem-wood = 119887011986311988711198671198872

Stem-bark = 119887011986311988711198671198872

Crown = 11988701198631198871LCL1198872

Total-tree = 1198870 (1198632119867)1198872

(2)





1(plusmnSE) 119887

2(plusmnSE)









(kg) CV () MRSE (kg) MR (kg) 119894119894

2

SUR

Roots 11198632119867 5600 349040 731758 02750 03227 01503

Stem wood 11198632119867 2217 1166327 940069 05181 11685 17454

Stem bark 11198632119867 minus2922 181996 1281809 08488 01751 00432 10028

Crown 11198632119867 8150 285040 488144 14814 minus01298 01087

Total tree 11198632119867 6319 2495561 1021272 02332 15366 144049




Roots = 11988710 + 119887111198632119867

Stem-wood = 11988720 + 119887211198632119867

Stem-bark = 11988730 + 119887311198632119867

Crown = 11988740 + 119887411198632119867


= (11988710+ 11988720+ 11988730+ 11988740)

+ (11988711+ 11988721+ 11988731+ 11988741)1198632119867

= 11988750+ 119887511198632119867

(3)





21198632LCL025




Roots = 11988710 + 119887111198632+ 11988712119867

Stem-wood = 11988720 + 119887211198632

Stem-bark = 11988730 + 119887311198632119867

Crown = 11988740 + 119887411198632LCL025

Total = (11988710 + 11988720 + 11988730 + 11988740) + (11988711 + 11988721)1198632

+ 119887311198632119867 + 119887

411198632LCL025 + 119887

12119867

= 11988750+ 119887511198632+ 119887521198632119867 + 119887

531198632LCL025 + 119887

54119867

(4)







119899+(1199090minus 119909)2

SS119909

119878 (119864 (1199100)) =119878 (119864 (119910

0))

119910119894

times 100


119910sdot119909radic1 +1

119899+(1199090minus 119909)2

SS119909

119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100


2

119910119894+ 2

SUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100


2

119910119894+ 2

NSUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2





Roots = 11988710 (1198632119867)11988711

Stem-wood = 119887201198631198872111986711988722

Stem-bark = 119887301198631198873111986711988732

Crown = 1198874111986311988742LCL11988743

Total = 11988710 (1198632119867)11988711

+ 119887201198631198872111986711988722

+ 119887301198631198873111986711988732 + 1198874111986311988742LCL11988743

(5)













Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887


()119878119910sdot119909

(kg)CV()

MRSE(kg)

MR(kg)
















119878119910sdot119909(Total) = radic

119888

sum

119894=1

1198782

119910sdot119909(119894)+ 2sumsum119878

119894119895 (6)





CV(Total) =

119878119910sdot119909(Total)



3 Results





0+ 11988711198632119867 which was found






Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887

2(plusmnSE) 119887

3(plusmnSE) 119887

4(plusmnSE)


2119867 02522 (plusmn06334) 00097 (plusmn00002)












2119867 00075 (plusmn00022) 10137 (plusmn00326)




Total tree 11198632119867



Treecomponent



1198941198942

SUR 2

NSUR








2119867 8244 2206 4624 01378 01769 00581

Stem wood 11198632119867 7247 6059 4883 01732 06599 05943

Stem bark 11198632119867 5284 1056 7438 02403 00930 00157 09906 mdash

Crown 11198632119867 8196 2722 4662 14330 minus01188 01053

Total tree 11198632119867 8688 9667 3956 00791 08109 91562


2119867 9276 1284 2692 01168 00805 00244

Stem wood 11198632119867 9227 3566 2874 00440 03116 01718

Stem bark 11198632119867 7812 685 4825 02084 00423 00072 mdash 47801

Crown 11198632119867 8527 2641 4523 08348 minus00049 00859

Total tree 11198632119867 6776 5332 2182 00321 04296 67590





000

1000

2000

3000

4000

0 50 100 150 200

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(a)

000

1000

2000

3000

4000

0 100 200 300 400 500

Resid

uals

()


minus4000

minus3000

minus2000

minus1000

(b)


000

2000

4000

6000

8000

Resid

uals

()

minus8000

minus6000

minus4000

minus2000

(c)

000

2000

4000

6000

8000

0 50 100 150 200Re

sidua

ls (


minus8000

minus6000

minus4000

minus2000

(d)

000

1000

2000

3000

0 200 400 600 800

Resid

uals

()


minus3000

minus2000

minus1000

(e)







000

2000

4000

6000

8000

0 20 40 60 80 100 120

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(a)

000

2000

4000

6000

8000

0 50 100 150 200 250

Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(b)

000

2000

4000

6000

8000

10000

00 50 100 150 200 250Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

2000

4000

6000

0 100 200 300 400 500 600

Resid

uals

()


minus6000

minus4000

minus2000

(e)



4 Discussion




000

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140Resid

uals

()


minus3000

minus4000

minus2000

minus1000

(a)

1000

2000

3000

4000

0000

50 100 150 200 250 300 350

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(b)

0002000400060008000

10000

0 5 10 15 20 25 30 35 40

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800Resid

uals

()


minus3000

minus2000

minus1000

(e)









0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660




minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712










0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics


























Roots = 1198870 + 11988711198632119867

Stem-wood = 1198870 + 11988711198632119867

Stem-bark = 1198870 + 11988711198632119867

Crown = 1198870 + 11988711198632LCL025

Total-tree = 1198870 + 11988711198632119867

(1)

Roots = 1198870 (1198632119867)1198872

Stem-wood = 119887011986311988711198671198872

Stem-bark = 119887011986311988711198671198872

Crown = 11988701198631198871LCL1198872

Total-tree = 1198870 (1198632119867)1198872

(2)





1(plusmnSE) 119887

2(plusmnSE)









(kg) CV () MRSE (kg) MR (kg) 119894119894

2

SUR

Roots 11198632119867 5600 349040 731758 02750 03227 01503

Stem wood 11198632119867 2217 1166327 940069 05181 11685 17454

Stem bark 11198632119867 minus2922 181996 1281809 08488 01751 00432 10028

Crown 11198632119867 8150 285040 488144 14814 minus01298 01087

Total tree 11198632119867 6319 2495561 1021272 02332 15366 144049




Roots = 11988710 + 119887111198632119867

Stem-wood = 11988720 + 119887211198632119867

Stem-bark = 11988730 + 119887311198632119867

Crown = 11988740 + 119887411198632119867


= (11988710+ 11988720+ 11988730+ 11988740)

+ (11988711+ 11988721+ 11988731+ 11988741)1198632119867

= 11988750+ 119887511198632119867

(3)





21198632LCL025




Roots = 11988710 + 119887111198632+ 11988712119867

Stem-wood = 11988720 + 119887211198632

Stem-bark = 11988730 + 119887311198632119867

Crown = 11988740 + 119887411198632LCL025

Total = (11988710 + 11988720 + 11988730 + 11988740) + (11988711 + 11988721)1198632

+ 119887311198632119867 + 119887

411198632LCL025 + 119887

12119867

= 11988750+ 119887511198632+ 119887521198632119867 + 119887

531198632LCL025 + 119887

54119867

(4)







119899+(1199090minus 119909)2

SS119909

119878 (119864 (1199100)) =119878 (119864 (119910

0))

119910119894

times 100


119910sdot119909radic1 +1

119899+(1199090minus 119909)2

SS119909

119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100


2

119910119894+ 2

SUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100


2

119910119894+ 2

NSUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2





Roots = 11988710 (1198632119867)11988711

Stem-wood = 119887201198631198872111986711988722

Stem-bark = 119887301198631198873111986711988732

Crown = 1198874111986311988742LCL11988743

Total = 11988710 (1198632119867)11988711

+ 119887201198631198872111986711988722

+ 119887301198631198873111986711988732 + 1198874111986311988742LCL11988743

(5)













Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887


()119878119910sdot119909

(kg)CV()

MRSE(kg)

MR(kg)
















119878119910sdot119909(Total) = radic

119888

sum

119894=1

1198782

119910sdot119909(119894)+ 2sumsum119878

119894119895 (6)





CV(Total) =

119878119910sdot119909(Total)



3 Results





0+ 11988711198632119867 which was found






Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887

2(plusmnSE) 119887

3(plusmnSE) 119887

4(plusmnSE)


2119867 02522 (plusmn06334) 00097 (plusmn00002)












2119867 00075 (plusmn00022) 10137 (plusmn00326)




Total tree 11198632119867



Treecomponent



1198941198942

SUR 2

NSUR








2119867 8244 2206 4624 01378 01769 00581

Stem wood 11198632119867 7247 6059 4883 01732 06599 05943

Stem bark 11198632119867 5284 1056 7438 02403 00930 00157 09906 mdash

Crown 11198632119867 8196 2722 4662 14330 minus01188 01053

Total tree 11198632119867 8688 9667 3956 00791 08109 91562


2119867 9276 1284 2692 01168 00805 00244

Stem wood 11198632119867 9227 3566 2874 00440 03116 01718

Stem bark 11198632119867 7812 685 4825 02084 00423 00072 mdash 47801

Crown 11198632119867 8527 2641 4523 08348 minus00049 00859

Total tree 11198632119867 6776 5332 2182 00321 04296 67590





000

1000

2000

3000

4000

0 50 100 150 200

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(a)

000

1000

2000

3000

4000

0 100 200 300 400 500

Resid

uals

()


minus4000

minus3000

minus2000

minus1000

(b)


000

2000

4000

6000

8000

Resid

uals

()

minus8000

minus6000

minus4000

minus2000

(c)

000

2000

4000

6000

8000

0 50 100 150 200Re

sidua

ls (


minus8000

minus6000

minus4000

minus2000

(d)

000

1000

2000

3000

0 200 400 600 800

Resid

uals

()


minus3000

minus2000

minus1000

(e)







000

2000

4000

6000

8000

0 20 40 60 80 100 120

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(a)

000

2000

4000

6000

8000

0 50 100 150 200 250

Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(b)

000

2000

4000

6000

8000

10000

00 50 100 150 200 250Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

2000

4000

6000

0 100 200 300 400 500 600

Resid

uals

()


minus6000

minus4000

minus2000

(e)



4 Discussion




000

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140Resid

uals

()


minus3000

minus4000

minus2000

minus1000

(a)

1000

2000

3000

4000

0000

50 100 150 200 250 300 350

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(b)

0002000400060008000

10000

0 5 10 15 20 25 30 35 40

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800Resid

uals

()


minus3000

minus2000

minus1000

(e)









0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660




minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712










0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics

















1(plusmnSE) 119887

2(plusmnSE)









(kg) CV () MRSE (kg) MR (kg) 119894119894

2

SUR

Roots 11198632119867 5600 349040 731758 02750 03227 01503

Stem wood 11198632119867 2217 1166327 940069 05181 11685 17454

Stem bark 11198632119867 minus2922 181996 1281809 08488 01751 00432 10028

Crown 11198632119867 8150 285040 488144 14814 minus01298 01087

Total tree 11198632119867 6319 2495561 1021272 02332 15366 144049




Roots = 11988710 + 119887111198632119867

Stem-wood = 11988720 + 119887211198632119867

Stem-bark = 11988730 + 119887311198632119867

Crown = 11988740 + 119887411198632119867


= (11988710+ 11988720+ 11988730+ 11988740)

+ (11988711+ 11988721+ 11988731+ 11988741)1198632119867

= 11988750+ 119887511198632119867

(3)





21198632LCL025




Roots = 11988710 + 119887111198632+ 11988712119867

Stem-wood = 11988720 + 119887211198632

Stem-bark = 11988730 + 119887311198632119867

Crown = 11988740 + 119887411198632LCL025

Total = (11988710 + 11988720 + 11988730 + 11988740) + (11988711 + 11988721)1198632

+ 119887311198632119867 + 119887

411198632LCL025 + 119887

12119867

= 11988750+ 119887511198632+ 119887521198632119867 + 119887

531198632LCL025 + 119887

54119867

(4)







119899+(1199090minus 119909)2

SS119909

119878 (119864 (1199100)) =119878 (119864 (119910

0))

119910119894

times 100


119910sdot119909radic1 +1

119899+(1199090minus 119909)2

SS119909

119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100


2

119910119894+ 2

SUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100


2

119910119894+ 2

NSUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2





Roots = 11988710 (1198632119867)11988711

Stem-wood = 119887201198631198872111986711988722

Stem-bark = 119887301198631198873111986711988732

Crown = 1198874111986311988742LCL11988743

Total = 11988710 (1198632119867)11988711

+ 119887201198631198872111986711988722

+ 119887301198631198873111986711988732 + 1198874111986311988742LCL11988743

(5)













Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887


()119878119910sdot119909

(kg)CV()

MRSE(kg)

MR(kg)
















119878119910sdot119909(Total) = radic

119888

sum

119894=1

1198782

119910sdot119909(119894)+ 2sumsum119878

119894119895 (6)





CV(Total) =

119878119910sdot119909(Total)



3 Results





0+ 11988711198632119867 which was found






Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887

2(plusmnSE) 119887

3(plusmnSE) 119887

4(plusmnSE)


2119867 02522 (plusmn06334) 00097 (plusmn00002)












2119867 00075 (plusmn00022) 10137 (plusmn00326)




Total tree 11198632119867



Treecomponent



1198941198942

SUR 2

NSUR








2119867 8244 2206 4624 01378 01769 00581

Stem wood 11198632119867 7247 6059 4883 01732 06599 05943

Stem bark 11198632119867 5284 1056 7438 02403 00930 00157 09906 mdash

Crown 11198632119867 8196 2722 4662 14330 minus01188 01053

Total tree 11198632119867 8688 9667 3956 00791 08109 91562


2119867 9276 1284 2692 01168 00805 00244

Stem wood 11198632119867 9227 3566 2874 00440 03116 01718

Stem bark 11198632119867 7812 685 4825 02084 00423 00072 mdash 47801

Crown 11198632119867 8527 2641 4523 08348 minus00049 00859

Total tree 11198632119867 6776 5332 2182 00321 04296 67590





000

1000

2000

3000

4000

0 50 100 150 200

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(a)

000

1000

2000

3000

4000

0 100 200 300 400 500

Resid

uals

()


minus4000

minus3000

minus2000

minus1000

(b)


000

2000

4000

6000

8000

Resid

uals

()

minus8000

minus6000

minus4000

minus2000

(c)

000

2000

4000

6000

8000

0 50 100 150 200Re

sidua

ls (


minus8000

minus6000

minus4000

minus2000

(d)

000

1000

2000

3000

0 200 400 600 800

Resid

uals

()


minus3000

minus2000

minus1000

(e)







000

2000

4000

6000

8000

0 20 40 60 80 100 120

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(a)

000

2000

4000

6000

8000

0 50 100 150 200 250

Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(b)

000

2000

4000

6000

8000

10000

00 50 100 150 200 250Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

2000

4000

6000

0 100 200 300 400 500 600

Resid

uals

()


minus6000

minus4000

minus2000

(e)



4 Discussion




000

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140Resid

uals

()


minus3000

minus4000

minus2000

minus1000

(a)

1000

2000

3000

4000

0000

50 100 150 200 250 300 350

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(b)

0002000400060008000

10000

0 5 10 15 20 25 30 35 40

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800Resid

uals

()


minus3000

minus2000

minus1000

(e)









0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660




minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712










0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics



















119899+(1199090minus 119909)2

SS119909

119878 (119864 (1199100)) =119878 (119864 (119910

0))

119910119894

times 100


119910sdot119909radic1 +1

119899+(1199090minus 119909)2

SS119909

119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100


2

119910119894+ 2

SUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2

119910119894= radic119891

119894(119887)1015840Σ119887119891119894(119887) 119878 (119864 (119910

0)) =119878 (119864 (119910

0))

119910119894

times 100


2

119910119894+ 2

NSUR119894119894120595119894 (120579119894) 119878 (1199100119894minus 119910) =

119878 (1199100119894minus 119910)

119910119894

times 100


2





Roots = 11988710 (1198632119867)11988711

Stem-wood = 119887201198631198872111986711988722

Stem-bark = 119887301198631198873111986711988732

Crown = 1198874111986311988742LCL11988743

Total = 11988710 (1198632119867)11988711

+ 119887201198631198872111986711988722

+ 119887301198631198873111986711988732 + 1198874111986311988742LCL11988743

(5)













Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887


()119878119910sdot119909

(kg)CV()

MRSE(kg)

MR(kg)
















119878119910sdot119909(Total) = radic

119888

sum

119894=1

1198782

119910sdot119909(119894)+ 2sumsum119878

119894119895 (6)





CV(Total) =

119878119910sdot119909(Total)



3 Results





0+ 11988711198632119867 which was found






Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887

2(plusmnSE) 119887

3(plusmnSE) 119887

4(plusmnSE)


2119867 02522 (plusmn06334) 00097 (plusmn00002)












2119867 00075 (plusmn00022) 10137 (plusmn00326)




Total tree 11198632119867



Treecomponent



1198941198942

SUR 2

NSUR








2119867 8244 2206 4624 01378 01769 00581

Stem wood 11198632119867 7247 6059 4883 01732 06599 05943

Stem bark 11198632119867 5284 1056 7438 02403 00930 00157 09906 mdash

Crown 11198632119867 8196 2722 4662 14330 minus01188 01053

Total tree 11198632119867 8688 9667 3956 00791 08109 91562


2119867 9276 1284 2692 01168 00805 00244

Stem wood 11198632119867 9227 3566 2874 00440 03116 01718

Stem bark 11198632119867 7812 685 4825 02084 00423 00072 mdash 47801

Crown 11198632119867 8527 2641 4523 08348 minus00049 00859

Total tree 11198632119867 6776 5332 2182 00321 04296 67590





000

1000

2000

3000

4000

0 50 100 150 200

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(a)

000

1000

2000

3000

4000

0 100 200 300 400 500

Resid

uals

()


minus4000

minus3000

minus2000

minus1000

(b)


000

2000

4000

6000

8000

Resid

uals

()

minus8000

minus6000

minus4000

minus2000

(c)

000

2000

4000

6000

8000

0 50 100 150 200Re

sidua

ls (


minus8000

minus6000

minus4000

minus2000

(d)

000

1000

2000

3000

0 200 400 600 800

Resid

uals

()


minus3000

minus2000

minus1000

(e)







000

2000

4000

6000

8000

0 20 40 60 80 100 120

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(a)

000

2000

4000

6000

8000

0 50 100 150 200 250

Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(b)

000

2000

4000

6000

8000

10000

00 50 100 150 200 250Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

2000

4000

6000

0 100 200 300 400 500 600

Resid

uals

()


minus6000

minus4000

minus2000

(e)



4 Discussion




000

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140Resid

uals

()


minus3000

minus4000

minus2000

minus1000

(a)

1000

2000

3000

4000

0000

50 100 150 200 250 300 350

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(b)

0002000400060008000

10000

0 5 10 15 20 25 30 35 40

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800Resid

uals

()


minus3000

minus2000

minus1000

(e)









0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660




minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712










0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics
















Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887


()119878119910sdot119909

(kg)CV()

MRSE(kg)

MR(kg)
















119878119910sdot119909(Total) = radic

119888

sum

119894=1

1198782

119910sdot119909(119894)+ 2sumsum119878

119894119895 (6)





CV(Total) =

119878119910sdot119909(Total)



3 Results





0+ 11988711198632119867 which was found






Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887

2(plusmnSE) 119887

3(plusmnSE) 119887

4(plusmnSE)


2119867 02522 (plusmn06334) 00097 (plusmn00002)












2119867 00075 (plusmn00022) 10137 (plusmn00326)




Total tree 11198632119867



Treecomponent



1198941198942

SUR 2

NSUR








2119867 8244 2206 4624 01378 01769 00581

Stem wood 11198632119867 7247 6059 4883 01732 06599 05943

Stem bark 11198632119867 5284 1056 7438 02403 00930 00157 09906 mdash

Crown 11198632119867 8196 2722 4662 14330 minus01188 01053

Total tree 11198632119867 8688 9667 3956 00791 08109 91562


2119867 9276 1284 2692 01168 00805 00244

Stem wood 11198632119867 9227 3566 2874 00440 03116 01718

Stem bark 11198632119867 7812 685 4825 02084 00423 00072 mdash 47801

Crown 11198632119867 8527 2641 4523 08348 minus00049 00859

Total tree 11198632119867 6776 5332 2182 00321 04296 67590





000

1000

2000

3000

4000

0 50 100 150 200

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(a)

000

1000

2000

3000

4000

0 100 200 300 400 500

Resid

uals

()


minus4000

minus3000

minus2000

minus1000

(b)


000

2000

4000

6000

8000

Resid

uals

()

minus8000

minus6000

minus4000

minus2000

(c)

000

2000

4000

6000

8000

0 50 100 150 200Re

sidua

ls (


minus8000

minus6000

minus4000

minus2000

(d)

000

1000

2000

3000

0 200 400 600 800

Resid

uals

()


minus3000

minus2000

minus1000

(e)







000

2000

4000

6000

8000

0 20 40 60 80 100 120

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(a)

000

2000

4000

6000

8000

0 50 100 150 200 250

Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(b)

000

2000

4000

6000

8000

10000

00 50 100 150 200 250Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

2000

4000

6000

0 100 200 300 400 500 600

Resid

uals

()


minus6000

minus4000

minus2000

(e)



4 Discussion




000

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140Resid

uals

()


minus3000

minus4000

minus2000

minus1000

(a)

1000

2000

3000

4000

0000

50 100 150 200 250 300 350

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(b)

0002000400060008000

10000

0 5 10 15 20 25 30 35 40

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800Resid

uals

()


minus3000

minus2000

minus1000

(e)









0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660




minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712










0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics
















Treecomponent


0(plusmnSE) 119887

1(plusmnSE) 119887

2(plusmnSE) 119887

3(plusmnSE) 119887

4(plusmnSE)


2119867 02522 (plusmn06334) 00097 (plusmn00002)












2119867 00075 (plusmn00022) 10137 (plusmn00326)




Total tree 11198632119867



Treecomponent



1198941198942

SUR 2

NSUR








2119867 8244 2206 4624 01378 01769 00581

Stem wood 11198632119867 7247 6059 4883 01732 06599 05943

Stem bark 11198632119867 5284 1056 7438 02403 00930 00157 09906 mdash

Crown 11198632119867 8196 2722 4662 14330 minus01188 01053

Total tree 11198632119867 8688 9667 3956 00791 08109 91562


2119867 9276 1284 2692 01168 00805 00244

Stem wood 11198632119867 9227 3566 2874 00440 03116 01718

Stem bark 11198632119867 7812 685 4825 02084 00423 00072 mdash 47801

Crown 11198632119867 8527 2641 4523 08348 minus00049 00859

Total tree 11198632119867 6776 5332 2182 00321 04296 67590





000

1000

2000

3000

4000

0 50 100 150 200

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(a)

000

1000

2000

3000

4000

0 100 200 300 400 500

Resid

uals

()


minus4000

minus3000

minus2000

minus1000

(b)


000

2000

4000

6000

8000

Resid

uals

()

minus8000

minus6000

minus4000

minus2000

(c)

000

2000

4000

6000

8000

0 50 100 150 200Re

sidua

ls (


minus8000

minus6000

minus4000

minus2000

(d)

000

1000

2000

3000

0 200 400 600 800

Resid

uals

()


minus3000

minus2000

minus1000

(e)







000

2000

4000

6000

8000

0 20 40 60 80 100 120

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(a)

000

2000

4000

6000

8000

0 50 100 150 200 250

Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(b)

000

2000

4000

6000

8000

10000

00 50 100 150 200 250Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

2000

4000

6000

0 100 200 300 400 500 600

Resid

uals

()


minus6000

minus4000

minus2000

(e)



4 Discussion




000

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140Resid

uals

()


minus3000

minus4000

minus2000

minus1000

(a)

1000

2000

3000

4000

0000

50 100 150 200 250 300 350

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(b)

0002000400060008000

10000

0 5 10 15 20 25 30 35 40

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800Resid

uals

()


minus3000

minus2000

minus1000

(e)









0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660




minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712










0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics















000

1000

2000

3000

4000

0 50 100 150 200

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(a)

000

1000

2000

3000

4000

0 100 200 300 400 500

Resid

uals

()


minus4000

minus3000

minus2000

minus1000

(b)


000

2000

4000

6000

8000

Resid

uals

()

minus8000

minus6000

minus4000

minus2000

(c)

000

2000

4000

6000

8000

0 50 100 150 200Re

sidua

ls (


minus8000

minus6000

minus4000

minus2000

(d)

000

1000

2000

3000

0 200 400 600 800

Resid

uals

()


minus3000

minus2000

minus1000

(e)







000

2000

4000

6000

8000

0 20 40 60 80 100 120

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(a)

000

2000

4000

6000

8000

0 50 100 150 200 250

Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(b)

000

2000

4000

6000

8000

10000

00 50 100 150 200 250Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

2000

4000

6000

0 100 200 300 400 500 600

Resid

uals

()


minus6000

minus4000

minus2000

(e)



4 Discussion




000

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140Resid

uals

()


minus3000

minus4000

minus2000

minus1000

(a)

1000

2000

3000

4000

0000

50 100 150 200 250 300 350

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(b)

0002000400060008000

10000

0 5 10 15 20 25 30 35 40

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800Resid

uals

()


minus3000

minus2000

minus1000

(e)









0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660




minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712










0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics















000

2000

4000

6000

8000

0 20 40 60 80 100 120

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(a)

000

2000

4000

6000

8000

0 50 100 150 200 250

Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(b)

000

2000

4000

6000

8000

10000

00 50 100 150 200 250Resid

uals

()


minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

2000

4000

6000

0 100 200 300 400 500 600

Resid

uals

()


minus6000

minus4000

minus2000

(e)



4 Discussion




000

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140Resid

uals

()


minus3000

minus4000

minus2000

minus1000

(a)

1000

2000

3000

4000

0000

50 100 150 200 250 300 350

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(b)

0002000400060008000

10000

0 5 10 15 20 25 30 35 40

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800Resid

uals

()


minus3000

minus2000

minus1000

(e)









0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660




minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712










0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics















000

1000

2000

3000

4000

5000

0 20 40 60 80 100 120 140Resid

uals

()


minus3000

minus4000

minus2000

minus1000

(a)

1000

2000

3000

4000

0000

50 100 150 200 250 300 350

Resid

uals

()


minus5000

minus4000

minus3000

minus2000

minus1000

(b)

0002000400060008000

10000

0 5 10 15 20 25 30 35 40

Resid

uals

()


minus10000

minus8000

minus6000

minus4000

minus2000

(c)

000

5000

10000

0 50 100 150 200 250

Resid

uals

()


minus10000

minus15000

minus5000

(d)

000

1000

2000

3000

4000

0 100 200 300 400 500 600 700 800Resid

uals

()


minus3000

minus2000

minus1000

(e)









0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660




minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712










0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics

















0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910) 119878(119864(119910

0)) 119878(119910

0119894minus 119910)

500 760 650 110 98935 107478 570913 573862 77570 94475800 916 212 704 24664 28828 77433 77598 57686 583641000 959 155 804 09218 13087 41622 41682 49674 498541250 1340 580 760 04477 06223 28034 28049 33916 339431500 1312 223 1089 07874 08454 20203 20209 31360 313701750 1395 807 588 10461 10676 18206 18209 24721 247262000 1385 460 925 11791 11906 17894 17895 21321 213242250 1304 600 704 12514 12590 17775 17775 20573 205752500 1453 450 1003 13547 13584 18523 18523 20828 208282750 1346 289 1057 13843 13873 19000 19000 22690 226903050 1505 216 1289 14515 14529 19571 19571 26660 26660




minus1 06255 01204 52 lt0000111988751= 11988711+ 11988721

minus1 22306100 3555158 627 lt0000111988752= 11988731

minus1 3904832 435058 898 lt0000111988753= 11988742

minus1 2270888 248863 913 lt0000111988754= 11988712










0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics















0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

Belo

wgr

ound

bio

mas

s (kg

)

DBH (cm)

CONSUR


(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35

Stem

woo

d bi

omas

s (kg

)

DBH (cm)


NSUR

(b)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Stem

bar

k bi

omas

s (kg

)

DBH (cm)


NSUR

(c)

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Crow

n bi

omas

s (kg

)

DBH (cm)


NSUR

(d)

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25 30 35

Tota

l tre

e bio

mas

s (kg

)

DBH (cm)


NSUR

(e)















5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics



























5 Conclusions




Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics
















Appendix







Acknowledgments


References




































































Journal of












Volume 2014

Advances in









Geophysics

























































Journal of












Volume 2014

Advances in









Geophysics














research article biomass modelling of androstachys johnsonii prain: a comparison...

Documents