site specific stem volume models for pinus patula and...

Research ArticleSite Specific Stem Volume Models forPinus patula and Pinus oocarpa

Herbert Malata1 Elisha S Ngulube1 and EdwardMissanjo2

1Department of Forestry Faculty of Environmental Sciences Mzuzu University Private Bag 201 Luwinga Mzuzu 2 Malawi2Department of Forestry Malawi College of Forestry and Wildlife Private Bag 6 Dedza Malawi

Correspondence should be addressed to Edward Missanjo edwardem2gmailcom

Received 1 July 2017 Revised 12 September 2017 Accepted 1 October 2017 Published 25 October 2017

Academic Editor Qing-Lai Dang

Copyright copy 2017 Herbert Malata et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Sustainable management of timber forests requires availability and adequacy of models for accurate estimation of tree volumesThis study was conducted to develop site specific models for estimating individual total tree stem volume of Pinus patula and Pinusoocarpa at Chongoni Timber Plantation in Central Malawi A total of 32 trees from Pinus patula compartment and 48 trees fromPinus oocarpa compartment were destructively sampled Various predictors including diameter at breast height (dbh) and height(ht) were run against total stem volume using a nonlinearmixed-effectsmodelling approachThe results indicate that the developedsite specific models showed a significant association between total stem volume and the predictors (dbh and ht) The developedvolume models accounted for at least 99 of the total variation in the total stem volume data This suggests that application of thedeveloped site specific models is highly recommended when accurate results are required The appropriateness of the developedmodels was also supported by the fact that the total relative errors (TRE) of these models were lower (range minus004 to 006) thanthe TRE of some previously developed models (range minus1240 to 4170) tested on the present data

1 Introduction

Most of the commercial timber plantations in central Malawiare planted with tropical pine trees The commonly plantedtimber species in these plantations include Pinus patula Pkesiya P elliottii and P oocarpa [1 2] Volume is customarilyused in these forest plantations as a standard measureon which timber pricing and yield are based Estimationof standing timber volume is traditionally done by usingallometric models Common procedures used in allometryare the direct volumetric measurements of the stem Vol-ume and tariff tables are developed for the estimation ofvolumetric stem content The implied conversion to someend-product procedure of volume determination (eg DoyleScriber or International Log Rules) is less popular inMalawirsquoscommercial timber plantations

Accurate estimation of biomass is a precursor to sus-tainable forest management [3ndash5] Biomass estimates playan important decision support mechanism in commercialexploitation of timber nontimber forest products and otherecosystem services [5] Models are vital for forest planning

yield estimation projection and regulation of harvests Todate generalized allometric models are commonly usedto estimate timber volume in Malawi These models aredesigned to cover wider spatial dimensions or extended toconditions that are sometimes dissimilar from localities oftheir origin However it is important to note that differenttimber species exhibit different growth responses to differentsite conditions and associated management prescriptions[6] Henceforth the usefulness of generalized models is notwithout some limitations for effective decision support inforest management

Although these models provide useful volume estimationinsights into most or wider forest management applica-tions [4] site and species specific volume modelling wouldprecisely guide operational decisions affecting commercialtimber plantation management in Malawi [7] Developmentof localised models would not only help to maximise timbervalue but also help to identify key variable constructs of themodel Plausible advocacy for use of localised modelling hasbeen reported in several studies [8ndash11] particularly where pre-cision and revenues are priorities This modelling approach

HindawiInternational Journal of Forestry ResearchVolume 2017 Article ID 3981647 6 pageshttpsdoiorg10115520173981647

2 International Journal of Forestry Research

Table 1 Characteristics of the stand

Variable Mean Minimum Maximum Standard deviationPinus patula (number of trees = 32)Diameter at breast height (cm) 195 140 340 441Tree height (m) 178 123 217 242Pinus oocarpa (number of trees = 48)Diameter at breast height (cm) 206 140 280 327Tree height (m) 153 123 197 198

yields accurate and reliable volume estimates for sustainabledecision support in the forest management [2 12] Howeverthe quality of a model estimate is only as good as the qualityof data variables from which the model is developed

The main objective of this study was to develop sitespecific models for estimating total tree volume of pinesat Chongoni Timber Plantation (CTP) in central Malawiusing mixed-effect modelling approach Specific objectivesof the study were to (i) develop total individual tree stemvolume models for P patula and P oocarpa and (ii) comparethe predictive performance between site specific and thegeneralized volume models at CTP

2 Materials and Methods

21 Study Site The studywas conducted at Chongoni TimberPlantation (CTP) in Dedza Central Malawi CTP covers anestimated area of 5270 ha located within Chongoni ForestReserve The reserve lies between the latitudes 14∘101015840S and14∘211015840S and longitudes 34∘091015840E and 34∘171015840E It receives amean annual rainfall in the range of about 1200mm to1800mm with mean annual temperatures ranging from 7∘Cto 25∘C The altitude of the reserves varies from 1570m to1690m above the sea level [13] The forest is dominated byferruginous and humic ferrallitic soils [14] characterised byhigh organic matter being leached and occurring at highaltitudes The study was carried out in compartments 3A ofP oocarpa (164 ha slope 7) and 19B of P patula (104 haslope 5)

22 History and Description of Forest Stands Both standswere established from nursery seedlings after harvesting ofthe first rotation crop Pinus oocarpa and P patula seedlingswere planted at the age of six months after pricking out(propagating plants sown on seed bed) in 1991 The meanheight and root collar diameter of the seedlings were 263 cmand 54mm respectively These seedlings were planted in 30times 30 cm hoe dug pits at a spacing of 275m times 275m (approx1320 stems haminus1)Thinning was carried out at the ages of 9 15and 19 years by removing 35 28 and 39 of the trees in astand respectively Pruningwas done at the ages of 4 9 and 15years to half of the stem heights in each caseThe stands werecharacterised by the following descriptive variables (Table 1)

23 Field Sampling and Data Collection A systematic sam-pling design with a randomly selected starting point was

used Thereafter plots were spaced at uniform intervals of200m along strips throughout the compartments Strips werespaced at 100m intervals This sampling design was chosento uniformly distribute the sample units over the entirepopulation [15]

The minimum required number of sample plots wasdetermined using the following formula [16]

119899 = 119886119901119904 (1)

where 119899 is the required number of sample plots 119886 is the areaof the compartment in ha 119901 is the sampling intensity and119904 is the plot size in ha In this study a sampling intensityof 3 (003) and sample plot size of 004 ha were used Atotal of 20 sample plots were established Out of these 12sample plots were determined inP oocarpa compartment and8 sample plots in P patula compartment After determiningthe number of sample plots square plots of 004 ha weresystematically laid down at every 200m throughout eachcompartment In each sample plot all standing trees wereassessed for diameter at breast height (dbh) (13m from theground) and their corresponding heights using a caliperand a Suunto clinometer respectively Every 5th tree wasselected for destructive sampling in each sample plot A totalof 4 trees in each plot were felled These trees were cutat 30 cm above ground on the buttress using a chain sawA total of 48 trees from P oocarpa compartment and 32trees from P patula compartment were destructively sampledfor log volume determination The total height of trees wasconfirmed on felled trees by using a 50m linear measuringtape The felled trees were marked into logs approximately30m long each (where applicable) up to the minimum top(5 cm) diameter Diameters at lower middle and top end ofeach log were measured using a caliper for the purpose ofestimating log volumeThe volume of each log was estimatedusing newtonrsquos formula This method was chosen in order tomaximise precision and accuracy of the volume due to taper[17] The equation used was

119881 = 120587(1198891198972 + 41198891198982 + 1198891199062240000 )119871 (2)

where 119881 is the volume in m3 of the log 119889119897 is the diameter atlower end of the log in cm 119889119898 is the diameter at the middleof the log in cm 119889119906 is the diameter at the upper end of thelog in cm and 119871 is the length in m of each log Total stem

International Journal of Forestry Research 3

volumewas estimated as the sumof volumes of all log sectionsas follows

119881 = 119905sum119894=1

V119894 (3)

where 119894 is the 119894th log section V is the log volume in m3 and 119905is the number of logs in that particular stem

24 Statistical Analysis Prior to analysis data were tested fornormality and homogeneity using Kolmogorov-Smirnov Dand normal probability graphical tests Thus the dependentvariable (volume) was plotted against each of the explanatoryvariables to examine the range and shape of the functionalrelationship and to assess the heterogeneity of the vari-ance The following general nonlinear model forms whichdescribed individual tree volume as a function of the diameterat breast height (dbh) and total height (ht) were fitted

119881 = 1198870 times (dbh2 times ht)1198871 (4)

119881 = 1198870 times dbh1198871 times ht1198872 (5)

119881 = 1198870 times (dbh2)1198871 times ht1198872 (6)

where 119881 is total stem tree volume over bark (m3) dbh is thediameter at breast height (cm) ht is total tree height (m) and1198870 1198871 and 1198872 are parameter estimates The general nonlinearforms used in this study have adequate mathematical prop-erties and have performed satisfactorily in previous studies[7 18ndash20]

Nonlinear regression procedure (NLP) in SAS software[21] was used to fit the models parameters The importanceof using NLP is well explained by Mugasha et al [7]However (4) to (6) were log transformed in order to addressheteroscedasticity [22 23] Selection of the best modelswas based on high adjusted coefficient of determination(1198772adj) low root mean square error (RMSE) and finally lowAkaike Information Criterion (AIC) The expressions forthese statistics are summarized as follows

1198772adj = 1 minus (119899 minus 1)sum (119910119894 minus 119910119894)2(119899 minus 119901)sum (119910119894 minus 119910)2RMSE = radicsum (119910119894 minus 119910119894)2119899 minus 119901AIC = 119899 log1205902 + 2119896 minusmin (119899 log1205902 + 2119896)

(7)

where 119910119894 are observed values 119910119894 are estimated values 119910 is themean value of the samples and 119899 is the number of samples 119901is the number of parameters to be estimated 119896 = 119901 + 1 and1205902 is found by the following formula

1205902 = sum (119910119894 minus 119910119894)2119899 (8)

Deviation in the predicted outputs was minimised bymultiplying the exponential of the outputs by a correctionfactor (CF) [22 23] CF was computed as follows

CF = exp(MSE2) (9)

where MSE is the mean square error of the regressionNonlinear mixed-effects method was then applied to

the ldquobestrdquo models which were fitted using the NLMIXEDprocedure in SAS [21] Parameters of the ldquobestrdquo modelwere estimated with and without the presence of randomparameter(s) Nonlinearmixed-effectsmodelling approach iswell explained by other researchers [13 18 20 24]

The selected models were evaluated by computing thetotal relative error (TRE) andmean predictor error as follows[25]

TRE = sum119910119894 minus sum119910119894sum119910119894 lowast 100MPE = 119905120572radicsum (119910119894 minus 119910119894)2 (119899 minus 119901)119910radic119899 lowast 100

(10)

where 119905120572 is the 119905 value at confidence level 120572 with 119899 minus 119901degrees of freedom If the value of TRE was less than thatof MPE then the developed volume model was consideredacceptable Furthermore a generic volume model developedby Ingram and Chipompha (see (11)) [26] for conifer species(cypress and pines) in Malawi was also evaluated on the dataIn addition Studentrsquos 119905-test was run to determine statisticaldifferences on total relative errors and mean tree volumebetween the developed volume models and the genericvolume model

ln (119881) = minus10228 + ln (dbh2ht) (11)

where ln is the natural logarithm119881 is the volume in m3 dbhis diameter at breast height in cm and ht is the total height inm

3 Results and Discussion

31 Model Selection Parameter estimates fit statistics anddeveloped total stem volume models for P patula and Poocarpa at CTP are presented in Table 2Themodels showed astatistically significant association between total stem volumeandpredictors (diameter at breast height andheight)Nonlin-ear model (see (4)) performed better for both P patula and Poocarpa

The model for P patula and P oocarpa accounted for atleast 95 and 86 of the total variation in the total stemvolume models respectively The variation for the modelsdeveloped is in line with the fact that essentially volumeof a tree is the function of diameter and height [27 28]Unfortunately height measurements for standing trees aregenerally difficult time consuming and costly as comparedto dbh [13] It must be appreciated however that precisiongoes with a cost For models that only use dbh there mustbe well known precise conversion factors that translate the


Table 2 Selected total stem volumemodels parameter estimates standard errors (SE) and statisticmeasures of fit forP patula and P oocarpa

Species Pinus patula Pinus oocarpaEstimated parameters 0 1 0 1minus01466 00000712 minus00455 00000368SE 00252 00000029 00166 000000221198772adj 0951 0869RMSE 0076 0046AIC 9207 4583CF 1003 1001119875 values lt0001 lt0001Model (corrected by CF) ln (119881) = ndash01437 + 71 lowast 10minus5 ln (dbh2ht) ln (119881) = ndash00444 + 37 lowast 10minus5 ln (dbh2ht)Note 1198870 is the intercept 1198871 is the gradient of the predictor variable 1198772adj is the adjusted coefficient of determination CF(120590) is the correction factor dbh is thediameter at breast height and ht is the total tree height ln is the natural logarithm 119881 is volume of a tree

specific relationship between dbh and height of the particulartimber species The lower values of CF (approximately 1)in the models indicate a significant relationship betweenvariables that is lack of fit of the models is negligible [29]The best selected models were then subjected to mixed-effectmodelling approach

32 Mixed-Effects Modelling Approach The mixed-effectsmodel for (4) after transformation is

ln119881 = ln (1198870 + 120579119894) + (1198871 + 120579119895) ln (dbh2 times ht) + 1205761015840 (12)

where 1198870 and 1198871 are fixed-effects regressions parameters 120579119894and 120579119895 are random parameters of the 119894th and 119895th variablesrespectively 1205761015840 = ln 120576 and 120576 is random error 119881 dbh and htare stem volume diameter at breast height and total heightrespectively The mixed-effects volume models for both Ppatula and P oocarpawere fitted using NLMIXED procedurein SAS [21] but the models failed to converge Then thenumber of random parameters was systematically reduced toachieve convergence Convergence of the models for both Ppatula andP oocarpawas achieved by summing upparameterldquo1198870rdquo to a random parameter (120579119894) Therefore the final mixed-effects model for both P patula and P oocarpa can be writtenas

ln119881 = 119886 + 1198871 ln (dbh2 times ht) + 1205761015840 (13)

where 119886 = ln(1198870 + 120579119894) Thus the predicted volume has tobe obtained by back-transforming equation (13) into originalvalues Since logarithmic transformations are known toinduce systematic biases in the final dependent variable [27]the back-transformed equation is legible for bias correctionusing the correction factor [22]

The parameter estimates and fit statistics obtained bynonlinear mixed-effects modelling approach are presentedin Table 3 The fit statistics 1198772adj increased by 231 whilethe RMSE and AIC decreased significantly by 105 and181 respectively by performing a mixed-effects modellingapproach without random parameters for P patula modelLikewise 1198772adj increased by 929 while the RMSE and AICdecreased significantly by 239 and 483 respectively

by performing a mixed-effects modelling approach withoutrandom parameters for P oocarpa model This indicatesthat models developed by mixed-effects procedure withoutrandom parameters are superior to those developed by non-mixed-effects approach Similar results were also reported byother researchers [20 24]

Further analysis indicates that fit statistics (1198772adj RMSEand AIC values) of the mixed-effects model with randomparameters were better than those of its fixed-effects counter-part For instance RMSE and AIC decreased significantly by132 and 268 respectively while 1198772adj increased by 257by including the random parameters for P patula volumemodel Similarly RMSE and AIC decreased significantlyby 314 and 422 respectively while 1198772adj increased by407 by including the random parameters for P oocarpavolume model The present results are in agreement withthose in literature [13 20 24 30ndash33] Missanjo and Mwale[13] andGuangyi et al [20] reported that inclusion of randomparameters in mixed-effects modelling approach increasespredictive ability of the model

33 Comparison betweenDeveloped andGeneralized Tree Vol-ume Models Results on the comparison between developedvolume models and the traditional (generalized) model arepresented in Table 4 The generalized model (see (11)) [26]is underestimated by 417 and overestimated by 124 ofmean tree volume in P patula and P oocarpa respectivelywhen applied at CTP The TRE for the developed modelsfor P patula and P oocarpa were not significantly differentfrom zero and were less than their corresponding MPE Thisindicates that the developed models are acceptable in thestudy area

It is clear from the results that the traditional model wasassociated with larger TRE than the developed models Thepresent findings are in agreement with those in literature [2728] For example generalizedmodel developed byChave et al[27] underestimated and overestimated volume in Rondo andDindili forests in Tanzania respectively compared with thesite specificmodels developed byMugasha et al [7] Similarlythe generalized model developed by Hawkins [34] underes-timated volume for Eucalyptus camaldulensis in Nepal thanthe site specific model developed by Mandal et al [28]


Table 3 Parameter estimates standard errors and values of the statistics for selectedmodel fitted by use ofmixed-effectsmodelling approach

Method Estimated parameters SE 119875 value 1198772adj RMSE AICPinus patula

1119887119900 minus12420 17420 lt0001

0973 0068 75401198871 12792 00448 lt00011205902119890 02718 00103 lt00012

119887119900 minus12987 02014 lt00010998 0059 55211198871 12631 00257 lt00011205902119890 02557 00639 00041205902120579 07131 00341 lt0001

Pinus oocarpa

1119887119900 minus12425 02360 lt0001

0958 0035 23711198871 12314 00639 lt00011205902119890 00764 00014 lt00012

119887119900 minus13368 02162 lt00010997 0024 13701198871 12579 00512 lt00011205902119890 00659 00135 lt00011205902120579 07118 02018 lt0001

Note Method 1 = selected model fitted without any random parameters Method 2 = selected model fitted with a random parameter 1205902120579 and 1205902119890 are variances

for random-effect and residual error respectively

Table 4 Performance of developed models versus the generic model on the modelling datalowastlowast

Species Model Mean tree volume (m3) MPE () TRE ()

Pinus patula ln (119881) = ndash122739 + 12631 ln (dbh2ht) 0376 plusmn 0058a 102 minus004nsln (119881) = ndash10228 + ln (dbh2ht) 0265 plusmn 0030b 3193 4170lowast

Pinus oocarpa ln (119881) = ndash126562 + 12579 ln (dbh2ht) 0224 plusmn 0018a 154 006nsln (119881) = ndash10228 + ln (dbh2ht) 0252 plusmn 0016a 2181 minus1240lowast

Note Mean volumes followed by the same letter within species significantly differ (119875 lt 005) lowastsignificantly different from zero (119875 lt 005) ns = not significantlydifferent from zero (119875 gt 005) lowastlowastwhole data set was used in modelling

The magnitude of variations in errors may be due to dif-ferences in site characteristics silvicultural practices andthe type of data used in the development of the allometry[29]

The significant deviation of the generalized model devel-oped by Ingram and Chipompha [26] in estimating volumefor both P patula and P oocarpa in the current area maybe a clear indication that the model was used in conditionsoutside its generation bounds Therefore care must be takenin choosing volume models for application in different typesof tree species and geographical areas [35] as this has thepotential to affect the real value of timber resources

4 Conclusion

The present study has developed total stem volume modelsfor P patula and P oocarpa The results of the statisticsof fit were generally good enabling one to use the modelswith confidence for estimation of total stem volume for Ppatula and P oocarpa in Chongoni Timber Plantation inMalawi Due to deviation associated with volume estimatesdeveloped from the generalized volume model applicationof the developed site specific models is highly recom-mended

Conflicts of Interest

The authors declare that there are no conflicts of interest inany form regarding the publication of this article

Acknowledgments

The authors are grateful to forestry staff at Dedza DistrictForestry Office for allowing the study to be conducted atChongoni Timber Plantation and also for the assistanceprovided during data collection

References

[1] A Tiarks E K S Nambiar and C Cossalter ldquoSite managementand productivity in tropical forest plantationsrdquo in OccasionalPaper No 16 CIFOR Bogor Indonesia 1998

[2] R Juma T Pukkala S de-Miguel andMMuchiri ldquoEvaluationof different approaches to individual tree growth and survivalmodelling using data collected at irregular intervals ndash a casestudy for Pinus patula in Kenyardquo Forest Ecosystems vol 1 article14 no 1 2014

[3] D Zianis P Muukkonen R Makipaa and M MencucciniBiomass and Stem Volume equations for tree Species in Europe


Silva Fennica Monographs 4 The Finnish Society of ForestScience and the Finnish Forest Research institute VantaaFinland 2005

[4] S Labrecque R A Fournier J E Luther and D Piercey ldquoAcomparison of four methods to map biomass from Landsat-TMand inventory data in western Newfoundlandrdquo Forest Ecologyand Management vol 226 no 1-3 pp 129ndash144 2006

[5] R M Lucas N Cronin A Lee M Moghaddam C Witte andP Tickle ldquoEmpirical relationships betweenAIRSARbackscatterand LiDAR-derived forest biomass Queensland AustraliardquoRemote Sensing of Environment vol 100 no 3 pp 407ndash4252006

[6] J P Skovsgaard and J K Vanclay ldquoForest site productivityA review of spatial and temporal variability in natural siteconditionsrdquo Forestry vol 86 no 3 pp 305ndash315 2013

[7] W A Mugasha E E Mwakalukwa E Luoga et al ldquoAllometricModels for Estimating Tree Volume and Aboveground Biomassin Lowland Forests of Tanzaniardquo Journal of Forestry Researchvol 2016 Article ID 8076271 13 pages 2016

[8] M S Watt D J Palmer H Dungey and M O KimberleyldquoPredicting the spatial distribution of Cupressus lusitanicaproductivity in New Zealandrdquo Forest Ecology and Managementvol 258 no 3 pp 217ndash223 2009

[9] A N Djomo A Ibrahima J Saborowski and G GravenhorstldquoAllometric equations for biomass estimations in Cameroonand pan moist tropical equations including biomass data fromAfricardquo Forest Ecology and Management vol 260 no 10 pp1873ndash1885 2010

[10] L Nunes S T Gower S D Peckham M Magalhaes D Lopesand F C Rego ldquoEstimation of productivity in pine and oakforests in northern Portugal using Biome-BGCrdquo Forestry vol88 no 2 pp 200ndash212 2015

[11] A N Djomo N Picard A Fayolle et al ldquoTree allometry forestimation of carbon stocks inAfrican tropical forestsrdquo Forestryvol 89 no 4 pp 446ndash455 2016

[12] C M Litton and J B Kauffman ldquoAllometric models forpredicting aboveground biomass in two widespread woodyplants in Hawaiirdquo Biotropica vol 40 no 3 pp 313ndash320 2008

[13] E Missanjo and G Mwale ldquoA mixed-effects height-diametermodel for pinus kesiyain Malawirdquo Journal of Biodiversity Man-agement and Forestry vol 3 no 2 2014

[14] P D Hardcastle A Preliminary Silvicultural Classification ofMalawi Forest Research institute of Malawi Zomba Malaw1978

[15] E T Avery and E H Burkhart ForestMeasurementsMcGraw-Hill companies USA 2002

[16] B Bredenkamp ldquoPlantation inventoryrdquo in South AfricanForestry Handbook D LOwen Ed vol 1 pp 161ndash166 SouthernAfrican Institute of Forestry Southern African 2000

[17] B Husch T W Beers and J W Kershaw Forest MensurationJohn Wiley amp Sons Inc NJ USA 4th edition 2003

[18] T M Magalhaes ldquoSite-specific height-diameter and stemvolume equations for Lebombo-ironwoodrdquo Annals of ForestResearch vol 60 no 2 2017

[19] F X Schumacher and F D S Hall ldquoLogarithmic expression oftimber-tree volumerdquo Journal of Agricultural Research vol 47 pp719ndash734 1933

[20] M Guangyi S Yujun X Hao and S De-Miguel ldquoA mixed-effects model with different strategies for modeling volumein cunninghamia lanceolata plantationsrdquo PLoS ONE vol 10article e0140095 no 10 2015

[21] SAS Institute SASSTAT Usersrsquos Guide Cary NC USA 9edition 2010

[22] W S Zeng W S Zeng and S Z Tang ldquoBias correction in log-arithmic regression and comparison with weighted regressionfor nonlinear modelsrdquo Nature Precedings 2011

[23] D Zianis P Muukkonen R Makipaa and M MencucciniBiomass and Stem Volume Equations for Tree Species in EuropeMonographs 4 Silva Fennica 2005

[24] E D S Vismara L Mehtatalo and J L F Batista ldquoLinearmixed-effects models and calibration applied to volumemodelsin two rotations of Eucalyptus grandis plantationsrdquo CanadianJournal of Forest Research vol 46 no 1 pp 132ndash141 2015

[25] W S Zeng L J Zhang X Y Chen Z C Cheng K XMa andZH Li ldquoConstruction of compatible and additive individual-treebiomass models for Pinus tabulaeformis in Chinardquo CanadianJournal of Forest Research vol 47 no 4 pp 467ndash475 2017

[26] C L Ingram and N W S Chipompha The Silvicultural GuideBook of Malawi FRIM Zomba Malawi 2nd edition 1987

[27] J Chave M Rejou-Mechain A Burquez et al ldquoImprovedallometric models to estimate the aboveground biomass oftropical treesrdquo GCB Bioenergy vol 20 no 10 pp 3177ndash31902014

[28] R A Mandal B K V Yadav K K Yadav I C Dutta and S MHaque ldquoDevelopment of allometric equation for biomass esti-mation of eucalyptus camaldulensis A study from SagarnathForestrdquo International Journal of Biodiversity and Ecosystems vol1 no 1 pp 001ndash007 2013

[29] S D Makungwa A Chittock D L Skole G Y Kanyama-Phiriand I H Woodhouse ldquoAllometry for biomass estimation inJatropha trees planted as boundary hedge in farmersrsquo fieldsrdquoForests vol 4 no 2 pp 218ndash233 2013

[30] M Sharma and J Parton ldquoHeight-diameter equations forboreal tree species in Ontario using a mixed-effects modelingapproachrdquo Forest Ecology and Management vol 249 no 3 pp187ndash198 2007

[31] R Calama and G Montero ldquoInterregional nonlinear height-diameter model with random coefficients for stone pine inSpainrdquo Canadian Journal of Forest Research vol 34 no 1 pp150ndash163 2004

[32] B Vargas-Larreta F Castedo-Dorado J G Alvarez-GonzalezM Barrio-Anta and F Cruz-Cobos ldquoA generalized height-diameter model with random coefficients for uneven-agedstands in El Salto Durango (Mexico)rdquo Forestry vol 82 no 4pp 445ndash462 2009

[33] Y J Lee D W Coble J K Pyo S H Kim and W K Lee ldquoAmixed-effects height-diameter model for Pinus densiflora treesin Gangwon Province Koreardquo Journal of Korean Forest Societyvol 98 pp 178ndash182 2009

[34] T Hawkins ldquoEucalyptus Camaldulensis Dalbergia Sissoo Aca-cia Auriculiformis and Cassia Siamea in the Central Bhabar-Teral ofNepalrdquoOxford Forestry InstituteOccasional vol 33 1987

[35] E Missanjo G Kamanga-Thole and D Bonongwe ldquoAllometricEquations for Estimation of Above Ground Biomass of Euca-lyptus Camaldulensisin Malawirdquo Journal of Basic and AppliedResearch International vol 2 no 2 pp 41ndash47 2015

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Table 1 Characteristics of the stand

Variable Mean Minimum Maximum Standard deviationPinus patula (number of trees = 32)Diameter at breast height (cm) 195 140 340 441Tree height (m) 178 123 217 242Pinus oocarpa (number of trees = 48)Diameter at breast height (cm) 206 140 280 327Tree height (m) 153 123 197 198

yields accurate and reliable volume estimates for sustainabledecision support in the forest management [2 12] Howeverthe quality of a model estimate is only as good as the qualityof data variables from which the model is developed

The main objective of this study was to develop sitespecific models for estimating total tree volume of pinesat Chongoni Timber Plantation (CTP) in central Malawiusing mixed-effect modelling approach Specific objectivesof the study were to (i) develop total individual tree stemvolume models for P patula and P oocarpa and (ii) comparethe predictive performance between site specific and thegeneralized volume models at CTP

2 Materials and Methods

21 Study Site The studywas conducted at Chongoni TimberPlantation (CTP) in Dedza Central Malawi CTP covers anestimated area of 5270 ha located within Chongoni ForestReserve The reserve lies between the latitudes 14∘101015840S and14∘211015840S and longitudes 34∘091015840E and 34∘171015840E It receives amean annual rainfall in the range of about 1200mm to1800mm with mean annual temperatures ranging from 7∘Cto 25∘C The altitude of the reserves varies from 1570m to1690m above the sea level [13] The forest is dominated byferruginous and humic ferrallitic soils [14] characterised byhigh organic matter being leached and occurring at highaltitudes The study was carried out in compartments 3A ofP oocarpa (164 ha slope 7) and 19B of P patula (104 haslope 5)

22 History and Description of Forest Stands Both standswere established from nursery seedlings after harvesting ofthe first rotation crop Pinus oocarpa and P patula seedlingswere planted at the age of six months after pricking out(propagating plants sown on seed bed) in 1991 The meanheight and root collar diameter of the seedlings were 263 cmand 54mm respectively These seedlings were planted in 30times 30 cm hoe dug pits at a spacing of 275m times 275m (approx1320 stems haminus1)Thinning was carried out at the ages of 9 15and 19 years by removing 35 28 and 39 of the trees in astand respectively Pruningwas done at the ages of 4 9 and 15years to half of the stem heights in each caseThe stands werecharacterised by the following descriptive variables (Table 1)

23 Field Sampling and Data Collection A systematic sam-pling design with a randomly selected starting point was

used Thereafter plots were spaced at uniform intervals of200m along strips throughout the compartments Strips werespaced at 100m intervals This sampling design was chosento uniformly distribute the sample units over the entirepopulation [15]

The minimum required number of sample plots wasdetermined using the following formula [16]

119899 = 119886119901119904 (1)

where 119899 is the required number of sample plots 119886 is the areaof the compartment in ha 119901 is the sampling intensity and119904 is the plot size in ha In this study a sampling intensityof 3 (003) and sample plot size of 004 ha were used Atotal of 20 sample plots were established Out of these 12sample plots were determined inP oocarpa compartment and8 sample plots in P patula compartment After determiningthe number of sample plots square plots of 004 ha weresystematically laid down at every 200m throughout eachcompartment In each sample plot all standing trees wereassessed for diameter at breast height (dbh) (13m from theground) and their corresponding heights using a caliperand a Suunto clinometer respectively Every 5th tree wasselected for destructive sampling in each sample plot A totalof 4 trees in each plot were felled These trees were cutat 30 cm above ground on the buttress using a chain sawA total of 48 trees from P oocarpa compartment and 32trees from P patula compartment were destructively sampledfor log volume determination The total height of trees wasconfirmed on felled trees by using a 50m linear measuringtape The felled trees were marked into logs approximately30m long each (where applicable) up to the minimum top(5 cm) diameter Diameters at lower middle and top end ofeach log were measured using a caliper for the purpose ofestimating log volumeThe volume of each log was estimatedusing newtonrsquos formula This method was chosen in order tomaximise precision and accuracy of the volume due to taper[17] The equation used was

119881 = 120587(1198891198972 + 41198891198982 + 1198891199062240000 )119871 (2)

where 119881 is the volume in m3 of the log 119889119897 is the diameter atlower end of the log in cm 119889119898 is the diameter at the middleof the log in cm 119889119906 is the diameter at the upper end of thelog in cm and 119871 is the length in m of each log Total stem



119881 = 119905sum119894=1

V119894 (3)









(7)


1205902 = sum (119910119894 minus 119910119894)2119899 (8)


CF = exp(MSE2) (9)





(10)


ln (119881) = minus10228 + ln (dbh2ht) (11)












ln119881 = 119886 + 1198871 ln (dbh2 times ht) + 1205761015840 (13)










1119887119900 minus12420 17420 lt0001

0973 0068 75401198871 12792 00448 lt00011205902119890 02718 00103 lt00012

119887119900 minus12987 02014 lt00010998 0059 55211198871 12631 00257 lt00011205902119890 02557 00639 00041205902120579 07131 00341 lt0001

Pinus oocarpa

1119887119900 minus12425 02360 lt0001

0958 0035 23711198871 12314 00639 lt00011205902119890 00764 00014 lt00012

119887119900 minus13368 02162 lt00010997 0024 13701198871 12579 00512 lt00011205902119890 00659 00135 lt00011205902120579 07118 02018 lt0001










4 Conclusion




Acknowledgments


References










































Journal of










Advances in
























119881 = 119905sum119894=1

V119894 (3)









(7)


1205902 = sum (119910119894 minus 119910119894)2119899 (8)


CF = exp(MSE2) (9)





(10)


ln (119881) = minus10228 + ln (dbh2ht) (11)












ln119881 = 119886 + 1198871 ln (dbh2 times ht) + 1205761015840 (13)










1119887119900 minus12420 17420 lt0001

0973 0068 75401198871 12792 00448 lt00011205902119890 02718 00103 lt00012

119887119900 minus12987 02014 lt00010998 0059 55211198871 12631 00257 lt00011205902119890 02557 00639 00041205902120579 07131 00341 lt0001

Pinus oocarpa

1119887119900 minus12425 02360 lt0001

0958 0035 23711198871 12314 00639 lt00011205902119890 00764 00014 lt00012

119887119900 minus13368 02162 lt00010997 0024 13701198871 12579 00512 lt00011205902119890 00659 00135 lt00011205902120579 07118 02018 lt0001










4 Conclusion




Acknowledgments


References










































Journal of










Advances in





























ln119881 = 119886 + 1198871 ln (dbh2 times ht) + 1205761015840 (13)










1119887119900 minus12420 17420 lt0001

0973 0068 75401198871 12792 00448 lt00011205902119890 02718 00103 lt00012

119887119900 minus12987 02014 lt00010998 0059 55211198871 12631 00257 lt00011205902119890 02557 00639 00041205902120579 07131 00341 lt0001

Pinus oocarpa

1119887119900 minus12425 02360 lt0001

0958 0035 23711198871 12314 00639 lt00011205902119890 00764 00014 lt00012

119887119900 minus13368 02162 lt00010997 0024 13701198871 12579 00512 lt00011205902119890 00659 00135 lt00011205902120579 07118 02018 lt0001










4 Conclusion




Acknowledgments


References










































Journal of










Advances in

























1119887119900 minus12420 17420 lt0001

0973 0068 75401198871 12792 00448 lt00011205902119890 02718 00103 lt00012

119887119900 minus12987 02014 lt00010998 0059 55211198871 12631 00257 lt00011205902119890 02557 00639 00041205902120579 07131 00341 lt0001

Pinus oocarpa

1119887119900 minus12425 02360 lt0001

0958 0035 23711198871 12314 00639 lt00011205902119890 00764 00014 lt00012

119887119900 minus13368 02162 lt00010997 0024 13701198871 12579 00512 lt00011205902119890 00659 00135 lt00011205902120579 07118 02018 lt0001










4 Conclusion




Acknowledgments


References










































Journal of










Advances in




























































Journal of










Advances in






















site specific stem volume models for pinus patula and...

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