Research ArticleAllometric Equations for Estimating Silk Oak(Grevillea robusta) Biomass in Agricultural Landscapes ofMaragua Subcounty Kenya

Omamo Augustine Owate 1 Mugo JosephMware2 andMwangi James Kinyanjui2

1Kenya Forest Service PO Box 30513-00100 Nairobi Kenya2School of Natural Resources Karatina University PO Box 1957 Karatina Kenya

Correspondence should be addressed to Omamo Augustine Owate augustineowateyahoocom

Received 23 April 2018 Revised 8 August 2018 Accepted 16 August 2018 Published 2 October 2018

Academic Editor Scott D Roberts

Copyright copy 2018 Omamo Augustine Owate et al 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

Grevillea robusta is widely interplanted with crops inMaragua subcounty a practice that enhances biomass quantities in farmlandsHowever quick tools for estimating biomass of such trees are lacking resulting in undervaluation of the farm product Thisstudy sought to develop allometric equations for estimating tree biomass using diameter at breast height (DBH) and tree heightas predictor variables Tree biomass was computed using thirty-three (33) trees randomly selected from 12 one hectare plotsestablished in each of the four agroecological zones (AEZs) DBH of all Grevillea robusta trees per plot was measured and threetrees were selected for destructive sampling to cover the variety of tree sizes Regression analysis was used to develop equationsrelating DBHtree height to biomass based on linear exponential power and polynomial functions The polynomial and thepower equations had the highest R2 lowest SEE and MRE values while DBH was the most suitable parameter for estimatingtree biomass The tree stem branches foliage and roots biomass comprised 5689 1411 667 and 2232 of the total treebiomass respectivelyThemean tree biomass density (12430plusmn184 ton haminus1) showed no significant difference (p=009) across AEZsimplying no difference in G robusta agroforestry stocks across the AEZ The allometric equations will support marketing of treeproducts by farmers and therefore better conservation and management of the tree resource

1 Introduction

Trees in agricultural ecosystems offset pressure on forestresources in conventional forests and therefore play a majorrole in sustaining the productivity of agricultural and forestedlandscapes They are a source of livelihood for the ruralcommunities providing wood and nonwood products likeresin honey medicine vegetables among others and are alsoimportant in conservation of biological diversity water andsoil conservation [1] They represent a vital source of foodfor many of the worldrsquos poorest people providing both stableand supplemental foods fodder and fuel for lighting andcooking and food processing Besides they are also importantin biological diversity conservation and mitigating climatechange through carbon sequestration [2]

Quantification of the amount of biomass andor carbonstored in trees presently is an important component inthe implementation of the emerging carbon credit suchas Reducing Emissions from Deforestation and Degrada-tion (REDD+) [3] Developing countries including Kenyacan benefit from REDD+ related mechanisms by providingaccurate information about their forest and tree resourcesREDD+ requires countries to establish measurement report-ing and verification (MRV) methods [4] This may consistsof inventory of foreststrees in sampled plots and applicationof appropriate allometric equations to estimate biomass [2]Biomass estimates eventually are converted into carbon andcarbon dioxide (CO

2) equivalents

Most of the small scale farmers in Maragua integratetrees (mainly Grevillea robusta) with crops in their farms

HindawiInternational Journal of Forestry ResearchVolume 2018 Article ID 6495271 14 pageshttpsdoiorg10115520186495271

2 International Journal of Forestry Research

The specific economic values of the trees planted in agri-cultural landscapes have not been fully explored Since nomarketing guidelines have been developed for the differenttree products prices of the products are normally determinedby agreements between the seller and the buyer and thisvaries from area to another size of tree or product and thetargeted use of the product In many cases such negotiationsdo not favor the farmer and lowers the value of the treethus demotivating farmers from planting trees A methodthat helps establish biomass stocks and provides accurateinformation about the available wood resources from thisspecies would help in its management and conservation andwould enhance the livelihoods of the farmers

Some allometric equations have been developed to esti-mate tree biomass quantities using easily measurable param-eters such as DBH and height [1ndash3] Henry et al [1] and Kuyaet al [5] constructed equations for estimating tree biomassin agricultural landscapes of western Kenya while Kinyanjuiet al [6] constructed an equation for inventory of the aboveground biomass in theMau Forest EcosystemofKenyaMugoet al [7] predicted stem diameter of open grown trees inwestern Kenya Since tree allometry varies from site to site[8] such equations may not be appropriate for the conditionsof Maragua subcounty in terms of agro ecological zonationand the purpose for which the trees are grown Here a varietyof wood products are marketed for various uses includingtimber firewood pole wood and fencing and some leaveshave been used as livestock fodder Hence to meet the studyarea specific needs for tree products and tree componentsit was necessary that equations for estimating G robustabiomass quantities in the farming landscapes of Maraguasubcounty are developed

The purpose of this study was to develop equationsrelating tree biomass with easily measurable parameters ofdiameter at breast height (DBH) and height as a quick toolfor valuation of tree productsThe study also sought to assessvariations of G robusta biomass among agroecological zonesof the study area as a basis for developing tree resourcemanagement plans

2 Materials and Methods

21 Study Area The study was done in Maragua subcountyof Murangrsquoa county in central Kenya (Figure 1) The areacovers 839 Km2 [9] between longitude 36∘ 301015840E and 37∘301015840Eand latitude 00∘301015840S and 1∘S The study area consists of fourupper midland agroecological zones (AEZ) as illustrated inTable 1 Such variations of altitude and climate are expectedto influence allometry and also biomass productivity of Grobusta trees

22 Physical and Topographic Features The study area is amajor source of numerous springs and rivers that drain intoRiver Tana through rivers Maragua Irati Sabasaba KabukuMakindi Thuki Thamuru andThika [9] The geology of thesubcounty consists of volcanic rocks of the Pleistocene ageand basement system rock of Achaean type Volcanic rocksoccupy thewestern part of the county bordering theAberdare

ranges while rocks of the basement system are in the easternpart Porous beds and disconformities within the volcanicrock system form important aquifers collecting and movingground water thus regulating water supply from wells andboreholes In the study area Jaetzold et al [10] classified anddescribed soils in AEZ as shown in Table 2

23 Land Use Activities Farmers in the study area haveactively adopted agroforestry [11] Land use systems rangefrom subsistence small holder farms to more cash croporiented farms which relatively range from 15 to 2 acresWoody vegetation forms part of the agricultural landscapewhich varies from single tree to small stands that consists ofmainly exotic trees and isolated indigenous trees managed indifferent ways [11] Trees are grown around the homesteadsin woodlots and croplands and along farm boundariesGithiomi et al [11] further stated that trees and shrubs aregrown around the homestead in woodlots and cropland andalong farm boundaries and that woodlots are in small monospecific clusters of trees mainly in lower areas of the studyarea According to Kuya et al [5] such land use activitiesinfluence the biomass of agricultural landscapes in differentways depending on management activities

24 Sampling Design Stratified systematic sampling wasused on a Geographical Information System (GIS) platformto select sampling sites in each of the AEZs Each AEZwas divided into three equal polygons and the centre ofeach polygon was used as the reference data collection point(Figure 2)The position of the data collection point identifiedon the GIS map was recorded (Table 3) transferred into aGPS and traced to the groundThe GPS readings were basedon the UTMUPS format in UTM zone 37S A one hectare(100 x 100 m) plot was established at the reference pointaligned to the North-South and East-West grids All the Grobusta trees in the plotwere recorded for diameter at 13 fromthe ground (DBH) and total height Three G robusta trees ineach plot were selected for destructive sampling based on aproportional allocation among size classes identified in theplot

25 Processing of Destructively Sampled Trees

251 Destructive Sampling All the G robusta trees selectedfor destructive sampling were categorized into DBH classesThe selected trees were uprooted onto tarpaulin sheets spreadon felling direction (to avoid loss of foliage) leaves strippedoff and debranched and total tree lengthheight (HT) mea-sured using a linear tape Each of the trees was then dividedinto components (trunk branches foliage and roots) and thetrunkwas cross cut tomanageable sizesThe tree componentswere weighed in the field and their fresh weight was recordedSamples were taken from the different components of thetree and their fresh weight was taken The samples weresubsequently oven-dried in the laboratory at 105∘C as guidedby [12]

Similarly the branches were trimmed cross cut andclassified into four diameter classes as 0 lt D lt 2 cm (Class

International Journal of Forestry Research 3

Figure 1 Study area Showing the location on Kenyan map and within the Murangrsquoa county

Figure 2 Maragua agroecological zones showing polygons per zone and points for data collection

4 International Journal of Forestry Research

Table 1 Biophysical and climatic conditions of Maragua subcounty (source [10])

Attribute Upper midland 1 (UM 1) Upper midland 2 (UM 2) Upper midland 3 (UM 3) Upper midland 4 (UM 4)Altitude range (m) 1730 - 2430 1500 ndash 1730 1340 ndash 1500 1060 - 1340Mean annual Rainfall (mm) 2200 15375 955 970Mean annual Temperature (∘C) 184∘C 193∘C 202 212

Table 2 Classification and description of soil in Maragua subcounty

AEZ Physiographic Lithology Soil description

UM 1 MV2Well drained very deep dark reddish to dark brown very friable and smeary clay loamto clay with thick acid humic topsoil in places shallow to moderately deep and rocky

Humic ANDOSOLS partly lithic phase

UM 2 RB1Well drained extremely deep dark reddish brown to dark brown friable and slightly

smeary clay with an acid humic topsoil Ando-humic NITISOLS with humicANDOSOLS

RB2 well drained extremely deep dusky red to dark reddish brown friable clay with an acidhumic topsoil humic NITISOL

UM 3 RB3

Well drained extremely deep dusky red to dark reddish brown friable clay with inclusionof well drained moderately deep dark red to dark reddish brown friable clay over rockpisoferric or petroferric materials Eutric NITISOLS with nito-chromic CAMBISOLSand chromic ACRISOLS and LUVISOLS partly lithic pisoferric or petroferric phase

UM 4 LB1 Well drained very deep dark red very friable clay Nito-rhodic FERRALSOLS

Table 3 Coordinates of data collection points for all the AEZs

Agroecological Zone Plot number Eastings (m) Nothings (m)

UM 41 305449791 99003082872 301575475 99087491653 297040133 9914658828

UM 31 290497054 98966631322 298551514 99030694503 289507887 9901526723

UM 21 281419488 99099827172 276445967 99045766373 268721854 9911103375

UM 11 263165408 98966631322 259196650 99185092813 256504015 9914786820

1) 2 le D lt 5 cm (Class 11) 5 le D lt 10 cm (Class 111) andDge 10 cm (Class IV) for easy of weighingTheir weights weretaken for green weight to the nearest 01 kg The heavier oneswere measured as individual billets while the lighter oneswere bundled together and weighed for their green weightAliquots were taken and labeled and their green weight wasrecorded to the nearest 001gm kept in bags and taken tothe laboratory for oven-dry (105∘C) weight measurementThe foliage was collected on to the tarpaulin sheet bundledinto gunny bags whose weights were known and weighedto the nearest 01kg Their green weights were calculated asthe difference between the gross weight and the weight ofthe empty gunny bags and recorded A sample of the foliagewas taken from the combined mass of the foliage weighedrecorded to the nearest 001gm and oven-dried (70∘C)

Excavation of the tree was done manually until all theroots were removedThe taproot was followed to its endpointand root length recorded Soil embedded in the stump jointsand on root surface was removed by use of a brush and waterThe roots were classified into size classes as (Class 1) 0 lt D lt2 cm (Class 11) 2 le D lt 10 cm and (Class 111) D ge10 cm forease of weighing Roots were weighed by size classes for greenweight and recorded An aliquot of each root size class wasextracted and weighed for green weight recorded taggedpackaged and taken to the laboratory to oven-dry at 105∘CIn all the cases the aliquots were left in the oven to dry andchanges in dry weight were monitored on a daily basis untilthey reached a constant weight

252 Biomass Measurement The aliquotrsquos green and oven-dry weights were used to get the dry-green weight ratiosThese were subsequently used to convert the green weight ofthe tree component (trunks branches foliage or roots) to dryweight which is the componentrsquos biomass The total above-ground (AGB) biomass was obtained by getting the sum ofthe biomass of the trunk branches and foliage Similarly thetotal belowground (BGB) biomass was obtained by summingup all the dry weights of all the root sections of that given treeFinally the total tree biomass (TTB) was obtained by addingup aboveground and belowground biomass Scatter plotsand function graphs were used in assessing the relationshipsbetween easilymeasurable variables of DBH andHT togetherwith a combination ofDBHandHT against total tree biomassand tree component biomass

253 Development of Biomass Equations Thirty-threedestructively sampled trees were used to develop the biomassestimation allometric equations The measured predictor

International Journal of Forestry Research 5

Table 4 Biomass partitions (Kg) of each component and total tree biomass of sampled trees for every AEZ

Zone Stem Branches Foliage AGB BGB TTBUM 1 55025 12984 8105 76114 16683 92795UM 2 101110 21845 8736 131691 37256 168947UM 3 120443 33289 14524 168256 53524 221784UM 4 83814 21313 10907 116084 33987 150061Total 360432 89431 42272 492545 141450 633589

Table 5 Percentage contribution to total tree biomass among tree components in the different AEZ

Zone Stem Branches Foliage AGB BGBUM 1 5930 1399 873 8202 1798UM 2 5985 1293 517 7795 2205UM 3 5431 1501 655 7586 2413UM 4 5585 1420 727 7736 2265Total 5689 1411 667 7774 2233

variables DBH height (Ht) and product of DBH and HT(DBHlowastHt) for each of the destructively sampled treeswere regressed to the dry weight (biomass) of the totaltree biomass (TTB) or component biomass [(AGB) (BGB)branches biomass (BR) and foliage biomass (F)]

Scatter plots were used in illustrating the relationshipsbetween total tree and tree component biomass with theeasily measurable variables To derive the equation for eachof the dependent variable (TTB AGB BGB BR and F) theregression functions (exponential linear polynomial andpower) were superimposed on the scatter plot graphs Theselection of the best fit equation was based on the loweststandard error of the estimate (SEE) which is the standarddeviation of the residuals the lowest residual mean error(RME) and the highest coefficient of determination (R2)

254 Validation of Developed Allometric Equations Themean differences between predicted and observed biomasswere used to test the suitability of the equation Simple linearregression analysis between observed and predicted values ofthe equations quantifies the tendency of residuals whereby R2and mean standard error (MSE) indicate the precision of theestimates Residual plots were also used to assist in the eval-uation of the equations Bias was computed as ((predictedbiomass-measured biomass)measured biomass)lowast 100 [13]

Finally the developed equation for total tree biomasswas compared with several equations in similar managementunits but different geographical areasThe two sets of biomassvalues were subjected to a paired t test [14] to find ifdifferences occur in each biomass estimate comparison

3 Results

31 Preliminary Findings of the Dataset A total of 1090 treeswere measured for DBH in the twelve (12) plots 222 in AEZ 1308 in AEZ2 292 in AEZ 3 and 268 in AEZ 4 The values forDBH ranged from 1cm to 395cm with a mean of 1108 cm inAEZ1 1151 cm in AEZ 2 1007 cm in AEZ 2 and 1214 cm in

AEZ 4Height values ranged from60m to 248mwith ameanof 1167m in AEZ 4 1332m in AEZ 3 1403m in AEZ 2 and1142m in AEZ 1 Out of the 1090 trees measured for DBH 33trees were destructively sampled for biomass measurements

32 Percentage Contributions of Different Tree ComponentsBiomass The summary distribution of the total tree biomassand tree biomass components of the thirty-three destruc-tively sampled trees of different sizes recorded in the studyarea are as shown in Tables 4 and 5 The total tree biomass(TTB) for the 33 trees was 633589 kg distributed as followsstemtrunk (5689) branches (1411) foliage (667) androots (2233)Thus aboveground biomass (AGB) comprised7774while belowground biomass (BGB) was 2233Theseare the proportions of biomass available for specific useseg timber (stem biomass) fuel wood (branches biomass)mulchlivestock feedgreen manure (foliage biomass) andsoil organic carbon services (roots)

The stem comprises the largest percentage of the totaltree biomass (Table 5) while foliage has the least biomasscontribution and this is in agreement with similar studies[1 5 15] The 2233 proportion of BGB is close to the IPCCdefault value for BGB which is taken as 24 [16] The slightvariations in allocation among AEZ could be a justificationfor development of very specific allometric equations for eachof theAEZ For example the results indicated a slight increasein BGBAGB ratio with altitude rise from UM1 (0219) toUM4 (0293) Such information on component ratios amongG robusta and which is based on tree allometry variationsrequires further research and supports its conservation andusage

33 Illustrations of Biomass Estimation from Various Func-tions Various functions were plotted and the biomass esti-mates done for each function The goodness of fit in eachregression was illustrated by the coefficient of determination(R2 value) which explains how close the measured data are to

6 International Journal of Forestry Research

Table 6 Allometric equations for estimating various biomass using DBH

Function Equations MRE R2 SEEExponential TTB = 1091e0150DBH -2910 084 457Power TTB = 1811DBH1658 505 098 134Polynomial TTB = 0322DBBH2+793DBH-1926 015 093 133Linear TTB= 1800DBH - 7322 007 091 152Multiple TTB = 11356DBH ndash 8924HT + 0536(DBHlowastHT) + 1827 -016 093 140Exponential AGB=8474e0150DBH -2260 083 356Power AGB=1384DBH1665 32 098 099Linear AGB=1399DBH - 5696 002 092 112Polynomial AGB=0248DBH2 + 6243DBH ndash 1545 0002 094 099Multiple AGB=8641DBH ndash 69HT + 0424(DBHlowastHT) + 1453 006 090 198Exponential BGB = 2311e0151DBH -513 082 104Polynomial BGB = 0074DBH2+1688DBH ndash 3791 010 082 050Linear BGB = 4013DBH - 1624 -001 081 053Multiple BGB =2713DBH ndash 2028HT + 0111(DBHlowastHT) +379 010 082 051Power BGB = 0401DBH1642 342 093 051

the fitted regression line [14]These illustrations are shown inFigures 3 4 and 5

A comparison of functions for estimating TTB fromDBHillustrates that the exponential function overestimates DBHfor a tree of 35cm DBH Though the other three functionshave a near similar estimate the R2 values favor the powerfunction (R2 = 097) and the polynomial function (R2= 093)Though the linear function gives relatives good R2 valueforesters have disqualified linear relationships because theydo not illustrate the ideal relationship between predictorvariables and biomass or volume over a wide diameter sizedistribution [8 16]

Estimation of total tree biomass from height variedgreatly among functions making it difficult to select the idealfunction The R2 values were also lower compared to thoseof using DBH as a predictor variable The same trend wasnoted in estimating ABG from tree height Noting that heightmeasurement in forests is difficult and the fact that farmerssell trees while standing the use of tree height may increasetree biomass or volume estimation costs while not increasingaccuracy of estimates As such trials of height as a biomass-predictor variable were discarded in favor of DBH which iseasy to measure and can be measured with high levels ofaccuracy [6 8]

DBH gives a good estimate of AGB based on R2 valueswith 098 for the power function and 094 for the polynomialfunction Kuya [5] identified power functions as most idealfor estimating AGB in western Kenya while Henry et al[1] preferred polynomial functions It has been found thateither of these functions is ideal based on the diametersize distribution [8] Kuya [5] preferred power functionsbecause of the large DBH size distribution which disqualifiespolynomial functions which often have two turning points[14] and may not define the biomass-predictor relationshipover a wide range of diameter sizes In this case where Grobusta does not grow to large sizes in the study area either a

polynomial or a power function becomes ideal based on thiscriteria of choice

34 Choice of Equation Based on Standard Error of Estimateand Mean Residual Error Apart from the coefficient ofdetermination the standard error of estimate (SEE) and themean residual error (MRE) have been used in choice ofappropriate regression equations [14] The SEE is a measureof the accuracy of predictionsmadewith a regression line andthe lower the value the better the accuracy of an allometricequation [8] Zar [14] also explains the mean residual erroras another measure of the accuracy of a regression equationSince residuals are differences between the data points andthe regression line the mean residual error refers to the errorthat is not explained by the regression line

The choice of equation based on the three statistics isillustrated for the various biomass components in Table 6

Though linear functions had the least MRE for TTB andBGB their previously described limitations [8 14] disqual-ifies them The polynomial functions have very small MREvalues in all estimated biomass components of TTB (015kg)AGB (0002Kg) and BGB (01Kg) illustrating their appropri-ateness based on this second selection criteria Exponentialfunctions have large mean bias in all functions and thisfurther illustrates their inappropriateness in this selectionA bias of less than 5 of the total tree biomass is withinacceptable range [16 17] and would provide the farmers withthe real value of the tree In this case the polynomial functionis very accurate with very minimal bias within the range ofdiameter sizes tested

Based on the SEE the polynomial function gave thelowest values at 133 for TTB 099 for ABG and 05 forBGBThis compared well with the power function which had134 for TTB 099 for AGB and 051 for BGB In this thirdselection criteria the polynomial function again takes bestpreference

International Journal of Forestry Research 7

y = 18005x - 73223Rsup2 = 091

Linear Function

y = 10915e01504x

Rsup2 = 08361

Exponential function

y = 03223x 2 + 79347x - 19265 Rsup2 = 093

polynomial function

y = 1811x1658

Rsup2 = 09769

Power function

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0200400600800

10001200

Biom

ass (

Kg)

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

Figure 3 Comparison of functions for estimating total tree biomass from DBH

y = 30725e02672x

Rsup2 = 07813

Exponential Function

y = 29775x - 19625 Rsup2 = 07373

0 10 20 30

Tree Height (m)

Linear Function

y = 00332x32166

Rsup2 = 08693

Power Functiony = 03387x2 + 20641x - 14234

Rsup2 = 0741

0 10 20 30

Tree Height (m)

Polynomial Function

0

500

1000

1500

2000

2500

Biom

ass (

Kg)

10 20 300Tree Height (m) minus200

minus1000

100200300400500600

Biom

ass (

Kg)

minus200

0

200

400

600

800

Biom

ass (

Kg)

0200400600800

10001200

Biom

ass (

Kg)

10 20 300Tree Height (m)

Figure 4 A comparison of functions for estimating total tree biomass from tree height

Based on the statistics Table 7 shows the list of preferredequations for estimating the different tree biomass compo-nents Though all the preferred equations are polynomialfunctions it should be noted that the power functions werethe next best alternative and their application has alreadybeen illustrated for agroforestry species of western Kenya [5]The limitation of two turning points observed in polynomialfunctions [14] may not apply in the study area where Grobusta grows because the trees do not grow beyond the40cm DBH size that was used in this study It is howeverrecommended that such equations should not be appliedwhere trees of bigger sizes grow

Table 7 A list of selected allometric equations for estimatingbiomass components

Biomass component EquationsTotal Tree TTB = 0322DBBH2+793DBH-1926Above ground AGB=0248DBH2 + 6243DBH ndash 1545Below ground BGB = 0074DBH2+1688DBH ndash 3791Branches BRA = 0030DBH2 + 1574DBH ndash 4984Foliage F = 004DBH2 + 1949DBH ndash 3134

8 International Journal of Forestry Research

y = 1384x16658

Rsup2 = 09798

Power function

y = 13992x - 56966 Rsup2 = 09177

0 10 20 30 40

DBH (cm)

Linear function

y = 84746e01506x

Rsup2 = 0833

Exponential function

y = 0248x2 + 62437x - 15451 Rsup2 = 09374

0 10 20 30 40

DBH (cm)

Polynomial function

0

200

400

600

800

Biom

ass (

Kg)

10 20 30 400DBH (cm) minus100

0

100

200

300

400

500

Biom

ass (

Kg)

minus100

0

100

200

300

400

500

Biom

ass (

Kg)

0

100

200

300

400

500

Biom

ass (

Kg)

10 20 30 400DBH (cm)

Figure 5 A comparison of functions for estimating above ground tree biomass from DBH

Table 8 A validation of the equation with similar equations using the F values of the paired t-test

Author F calculated F critical Comments Discussion

Kuya [5] 15375557 18283There is nosignificantdifference

The Kuya equation was developed insimilar Agroforestry conditions but in a

different AEZs of Kenya

Henry [1] 0817302 18283There is nosignificantdifference

The equation was developed forAgroforestry trees of Western Kenya in a

different AEZ

Benedicto [19] 2070408 18408There is asignificantdifference

The equation was developed in Mexico Atotally different biome and may not be

applicable in the study area

Rurangwa [18] 1118687 18408There is nosignificantdifference

Rurangwa developed this equation inAgroforestry trees of Ruanda which is

within East Africa

Table 9 Average biomass values per hectare in AEZs

Component Average biomass (Kg) per hectareUM 1 UM 2 UM 3 UM 4

Foliage 922128 874343 724966 788837Branchesfoliage 1964818 1849623 1533623 1668739Rootsbelowground biomass 3109676 2927150 2427314 2640889Stemtrunk 7929378 7457484 6183147 6728175Total for tree 1392600 1310860 1086905 1182664

35 Validation of Developed Allometric Equations Validationof the equations based on the bias of the equation inestimating specific diameter sizes is illustrated in residualplots used to assist in validation which are shown in Figure 6

A second validation to compare biomass estimates fromthe preferred equation and that of similar studies showsthat the developed equation compares well with otherequations developed in agroforestry conditions of Kenya

[1 5] and Rwanda [18] but is not applicable in biomes farfrom the study area [19] This finding illustrates that theprocess of destructive sampling to develop new allomet-ric equations within a small geographical range may notenhance accuracy of estimates and an equation applicablein a similar land and tree management activity may as wellbe applicable in another one The results are illustrated inTable 8

International Journal of Forestry Research 9

0 10 20 30 40

DBH (cm)

Difference (Kg) Power function

0 10 20 30 40

DBH (cm)

Difference (Kg) Polynomial function

minus100

minus50

0

50

100Bi

omas

s res

idua

ls (k

g)

minus150

minus100

minus50

0

50

Biom

ass r

esid

uals

(kg)

Figure 6 Residual scatter plots of total tree biomass using polynomial and power function for TTB

Table 10 Total tree biomass and tree component biomass data of the 33 trees destructively sampled per every Agroecological Zone (AEZ)

AEZ Tree No DBH (cm) Height (m) Dry weights of biomass in kgStem Branches foliage AGB BGB TTB

UM4

1 52 655 1016 1625 522 1701 382 20832 15 36 155 0644 102 331 0801 4013 12 143 9369 1062 121 11641 3743 153844 132 127 7022 1108 1749 9879 2346 122255 225 167 16666 503 2292 23988 6314 303026 298 145 24752 8042 2127 34921 11955 468767V 18 60 165 033 0662 264 1461 4108V 137 145 11222 2661 1464 15347 3242 185899V 20 161 13487 315 1375 18012 5779 23791

UM3

10 120 1275 5901 688 1314 7903 324 1114311 154 137 1094 2475 2065 1548 5363 2084312 70 865 2038 50 75 3288 983 427113 56 865 1268 28 413 1961 594 255514 276 190 27053 9298 1797 38148 13037 5118515 277 192 30655 8325 160 4058 12708 5328816V 169 122 11803 4365 2239 18407 8603 270117V 98 91 3269 100 102 5289 1501 679418V 258 166 27516 6358 3326 3720 7495 44695

UM2

19 17 71 195 06 145 40 179 57920 87 98 2498 643 875 4016 786 480221 153 143 5883 385 1551 11284 2146 1343022 148 150 6963 3271 1046 1128 3399 1467923V 122 124 4063 1393 135 6806 1775 858124V 128 154 6294 1915 70 8909 2726 1163525 220 170 16471 3003 1109 20583 6836 2741926 298 212 2598 332 1089 30389 7934 3832327V 278 248 32763 439 871 38024 11475 49499

UM1

28 20 60 321 094 119 534 101 63529 89 99 2887 1025 1001 4913 590 550330V 45 91 1196 25 386 1832 360 219231 128 130 11466 3150 3122 17738 6522 242632 249 190 26284 3775 1857 31916 5650 3756633 204 115 12871 469 162 19181 3460 22641

10 International Journal of Forestry Research

Table 11 Allometric equations for estimating branch biomass using DBH

Function Equation MRE R2 SEEExponential BR = 4644e0069Dbh 1172 093 075Logarithmic BR = 1056ln(DBH) +1534 002 084 072Polynomial BR = 0077DBH2 + 3373DBH +0213 - 453 099 058Linear BR = 0941DBH+ 1324 003 096 073Power BR = 1901DBH0793 1159 099 073s

Table 12 Allometric equations for estimating foliage using DBH

Function Equation MRE R2 SEEExponential F = 4795e0045DBH 274 097 024Logarithmic F = 362ln(DBH) + 4020 002 084 022Polynomial F = -0031DBH2 + 1270DBH + 3235 -183 099 058Linear F = 0295DBH + 8452 0003 097 023Power F= 2213DBH0596 -237 098 023

Table 13 Allometric equations for estimating TTB using HT

Function Equation MRE R2 SEEExponential TTB = 3090e0266HT -3750 054 1010Logarithmic TTB = 3157ln(HT) ndash 5973 006 093 300Polynomial TTB = -00409HT2 + 1863HT + 1327 021 099 252Linear TTB = 2969HT- 1980 002 074 255Power TTB= 0401HT1642 -544 097 053

Table 14 Allometric equations for estimating AGB using HT

Function Equation MRE R2 SEEExponential AGB = 2454e0263HT -2437 054 744Logarithmic AGB = 2401ln(H) ndash 4526 0084 093 248Polynomial AGB= -0312HT2 + 1411HT- 9872 024 099 210Linear AGB= 2255HT-14850 002 070 212Power AGB= 0027HT3174 793 082 286

Table 15 Allometric equations for estimating BGB using HT

Function Equation MRE R2 SEEExponential BGB = 0631e0269HT -622 053 226Logarithmic BGB = 707ln(HT) - 1333 -004 093 079Polynomial BGB = -0067HT2 + 4781HTndash3258 015 1 071Linear BGB = 6009HTndash4345 010 064 2352Power BGB= 0006HT3241 584 080 3134

Table 16 Allometric equations for estimating TTB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential TTB= 2348e0006P -761 073 667Logarithmic TTB= 1077ln(P) - 3397 0002 072 285Polynomial TTB = -0000P2 + 111Pndash205 -402 I 252Linear TTB = 0829Pndash0929 006 090 158Power TTB= 0395P1125 215 098 268

International Journal of Forestry Research 11

Table 17 Allometric equations for estimating AGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential AGB = 1826e00006P -746 073 524Logarithmic AGB = 8222ln(P) ndash 2581 -688 072 231Polynomial AGB = -0000P2 + 0829Pndash1609 -29 1 185Linear AGB = 0630P + 0965 019 086 146Power AGB= 0310P1119 3837 099 152

Table 18 Allometric equations for estimating BGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential BGB = 495e00006P 134 073 -145Logarithmic BGB = 2424ln(P) ndash 7622 001 072 075Polynomial BGB = -0000P2 + 0255Pndash5495 -101 1 069Linear BGB = 0184P + 0575 007 078 075Power BGB= 0084P1125 306 099 075

Table 19 Generated TTB from developed equation using DBH

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM128 1295594 139 1474242 186 2336786 303 518241424 418944 1 6674 17 20251 298 50404221 6674 92 7725136 91 7593304 1 66741 6674 1 6674 188 2377058 44 221838444 2218384 1 6674 146 1592514 265 414892154 173205 135 140826 185 231676 1 667416 183976 1 6674 25 502 1 667410 8806 16 183976 16 183976 1 667410 8806 3 9282 194 2499618 16 18397613 132742 154 173205 108 9933456 18 221772128 1295594 215 294922 153 1714354 135 140826209 2817486 17 142064 128 1295594 1 667422 255016 122 1201862 162 1876246 148 162696219 241762 8 61912 209 2817486 175 212052 094 876 7150521 19 241762 16 18397689 7331824 13 132742 22 255016 15 1661714 371576 1 6674 78 5945736 185 23167612 520944 1 6674 52 3019696 14 149092165 193152 1 6674 45 2316 165 193152126 1264058 15 2958 45 2316 126 1264058153 1714354 1 6674 24 418944 153 171435413 132742 2 094 42 2025336 1 6674118 114083 97 8395216 51 2916984 13 13274214 371576 96 8259744 25 502 118 11408333 1192656 122 1201862 45 2316 145 1575415 2958 87 7073256 54 3227304 171 20440342 094 83 6564856 26 585784 1 66741 6674 109 1007766 1 6674 1 6674171 2044034 68 4762096 1 6674 18 221772171 2044034 69 4877184 9 74622 1 6674

12 International Journal of Forestry Research

Table 19 Continued

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM9 74622 29 841504 105 95052 124 1232814114 1080962 1 6674 46 2414344 114 1080962108 9933456 51 2916984 1 6674 108 993345611 102226 11 102226 1 6674 93 7857696105 95052 1 6674 1 6674 118 11408312 11712 12 11712 1 6674 156 17676627 4993 104 9363904 1 6674 7 4993122 1201862 52 3019696 7 4993 175 21205111 1036826 111 1036826 53 3123136 144 155835813 132742 61 3976864 13 446624 118 11408310 8806 1 6674 18 064104 10 8806128 1295594 128 1295594 1 6674 13 13274220 26248 68 4762096 1 6674 8 619121 6674 1 6674 1 6674 138 1457638104 9363904 1 6674 1 6674 114 108096214 149092 1 6674 98 8531416 154 17320516 183976 104 9363904 1 6674 84 6690864195 25203 62 4086856 1 6674 78 594573681 6315024 95 8125 28 755536 225 3174656 3437824 85 68176 49 2713744 1 667452 3019696 65 44212 42 2025336 156 176766210 8806 81 6315024 121 1186494 1 667413 132742 1 6674 87 7073256 1 6674169 2006238 1 6674 56 3437824 29 84150421 283926 82 6439576 1 6674 136 142464621 283926 57 3544176 15 16617 164 191302213 132742 1 6674 202 266711 1 667439 1741224 6 38676 297 5012242 1 6674173 2082122 1 6674 195 25203 17 2025116 183976 1 6674 23 329002 16 18397616 183976 1 6674 23 336616 187 235688621 283926 64 4309024 183 2276926 104 9363904187 2356886 48 2613216 12 11712 122 120186239 1741224 1 6674 54 3227304 13 132742132 1359538 1 6674 132 1359538 18 22177218 221772 1 6674 2 094 1 667458 3651256 15 2958 1 6674 1 6674

36 Biomass Stocks amongAgroecological Zones Based on theallometric equations the average TTB for G robusta treesgenerated in each of the AEZ studied is as shown in Table 9The TTB stock for each AEZ was 13 926 tonhaminus1 13109tonhaminus1 10869 tonhaminus1 and 11827 tonhaminus1 in UM1 UM2UM3 and UM4 respectively Variability of tree biomassbetween the four agroecological zones showed no significantdifference (p-value gt 005) implying that though there couldbe a slight difference in the allometry of the tree speciesamong AEZ the total biomass does not vary This alsoexplains that the management of G robusta trees in the

agricultural landscapes of the four AEZ does not differ andthe farmers can form a marketing unit despite their differentAEZ and their production quotas can be the same

The average biomass stock of 1243 tonha in the studycompares well with the findings of Albrecht [20] 2-22tonha Henry [1] 9ndash11tonha and Kuya [5] 16 tonhaall of which are for agricultural landscapes This findinggives a better glimpse of the tree component in agricul-tural landscapes and is a good guide for the develop-ment of carbon stock factors in agricultural landscapes[21] With this moderate stock the farmers are able to

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

International Journal of Forestry Research 3

Figure 1 Study area Showing the location on Kenyan map and within the Murangrsquoa county

Figure 2 Maragua agroecological zones showing polygons per zone and points for data collection

4 International Journal of Forestry Research

Table 1 Biophysical and climatic conditions of Maragua subcounty (source [10])

Attribute Upper midland 1 (UM 1) Upper midland 2 (UM 2) Upper midland 3 (UM 3) Upper midland 4 (UM 4)Altitude range (m) 1730 - 2430 1500 ndash 1730 1340 ndash 1500 1060 - 1340Mean annual Rainfall (mm) 2200 15375 955 970Mean annual Temperature (∘C) 184∘C 193∘C 202 212

Table 2 Classification and description of soil in Maragua subcounty

AEZ Physiographic Lithology Soil description

UM 1 MV2Well drained very deep dark reddish to dark brown very friable and smeary clay loamto clay with thick acid humic topsoil in places shallow to moderately deep and rocky

Humic ANDOSOLS partly lithic phase

UM 2 RB1Well drained extremely deep dark reddish brown to dark brown friable and slightly

smeary clay with an acid humic topsoil Ando-humic NITISOLS with humicANDOSOLS

RB2 well drained extremely deep dusky red to dark reddish brown friable clay with an acidhumic topsoil humic NITISOL

UM 3 RB3

Well drained extremely deep dusky red to dark reddish brown friable clay with inclusionof well drained moderately deep dark red to dark reddish brown friable clay over rockpisoferric or petroferric materials Eutric NITISOLS with nito-chromic CAMBISOLSand chromic ACRISOLS and LUVISOLS partly lithic pisoferric or petroferric phase

UM 4 LB1 Well drained very deep dark red very friable clay Nito-rhodic FERRALSOLS

Table 3 Coordinates of data collection points for all the AEZs

Agroecological Zone Plot number Eastings (m) Nothings (m)

UM 41 305449791 99003082872 301575475 99087491653 297040133 9914658828

UM 31 290497054 98966631322 298551514 99030694503 289507887 9901526723

UM 21 281419488 99099827172 276445967 99045766373 268721854 9911103375

UM 11 263165408 98966631322 259196650 99185092813 256504015 9914786820

1) 2 le D lt 5 cm (Class 11) 5 le D lt 10 cm (Class 111) andDge 10 cm (Class IV) for easy of weighingTheir weights weretaken for green weight to the nearest 01 kg The heavier oneswere measured as individual billets while the lighter oneswere bundled together and weighed for their green weightAliquots were taken and labeled and their green weight wasrecorded to the nearest 001gm kept in bags and taken tothe laboratory for oven-dry (105∘C) weight measurementThe foliage was collected on to the tarpaulin sheet bundledinto gunny bags whose weights were known and weighedto the nearest 01kg Their green weights were calculated asthe difference between the gross weight and the weight ofthe empty gunny bags and recorded A sample of the foliagewas taken from the combined mass of the foliage weighedrecorded to the nearest 001gm and oven-dried (70∘C)

Excavation of the tree was done manually until all theroots were removedThe taproot was followed to its endpointand root length recorded Soil embedded in the stump jointsand on root surface was removed by use of a brush and waterThe roots were classified into size classes as (Class 1) 0 lt D lt2 cm (Class 11) 2 le D lt 10 cm and (Class 111) D ge10 cm forease of weighing Roots were weighed by size classes for greenweight and recorded An aliquot of each root size class wasextracted and weighed for green weight recorded taggedpackaged and taken to the laboratory to oven-dry at 105∘CIn all the cases the aliquots were left in the oven to dry andchanges in dry weight were monitored on a daily basis untilthey reached a constant weight

252 Biomass Measurement The aliquotrsquos green and oven-dry weights were used to get the dry-green weight ratiosThese were subsequently used to convert the green weight ofthe tree component (trunks branches foliage or roots) to dryweight which is the componentrsquos biomass The total above-ground (AGB) biomass was obtained by getting the sum ofthe biomass of the trunk branches and foliage Similarly thetotal belowground (BGB) biomass was obtained by summingup all the dry weights of all the root sections of that given treeFinally the total tree biomass (TTB) was obtained by addingup aboveground and belowground biomass Scatter plotsand function graphs were used in assessing the relationshipsbetween easilymeasurable variables of DBH andHT togetherwith a combination ofDBHandHT against total tree biomassand tree component biomass

253 Development of Biomass Equations Thirty-threedestructively sampled trees were used to develop the biomassestimation allometric equations The measured predictor

International Journal of Forestry Research 5

Table 4 Biomass partitions (Kg) of each component and total tree biomass of sampled trees for every AEZ

Zone Stem Branches Foliage AGB BGB TTBUM 1 55025 12984 8105 76114 16683 92795UM 2 101110 21845 8736 131691 37256 168947UM 3 120443 33289 14524 168256 53524 221784UM 4 83814 21313 10907 116084 33987 150061Total 360432 89431 42272 492545 141450 633589

Table 5 Percentage contribution to total tree biomass among tree components in the different AEZ

Zone Stem Branches Foliage AGB BGBUM 1 5930 1399 873 8202 1798UM 2 5985 1293 517 7795 2205UM 3 5431 1501 655 7586 2413UM 4 5585 1420 727 7736 2265Total 5689 1411 667 7774 2233

variables DBH height (Ht) and product of DBH and HT(DBHlowastHt) for each of the destructively sampled treeswere regressed to the dry weight (biomass) of the totaltree biomass (TTB) or component biomass [(AGB) (BGB)branches biomass (BR) and foliage biomass (F)]

Scatter plots were used in illustrating the relationshipsbetween total tree and tree component biomass with theeasily measurable variables To derive the equation for eachof the dependent variable (TTB AGB BGB BR and F) theregression functions (exponential linear polynomial andpower) were superimposed on the scatter plot graphs Theselection of the best fit equation was based on the loweststandard error of the estimate (SEE) which is the standarddeviation of the residuals the lowest residual mean error(RME) and the highest coefficient of determination (R2)

254 Validation of Developed Allometric Equations Themean differences between predicted and observed biomasswere used to test the suitability of the equation Simple linearregression analysis between observed and predicted values ofthe equations quantifies the tendency of residuals whereby R2and mean standard error (MSE) indicate the precision of theestimates Residual plots were also used to assist in the eval-uation of the equations Bias was computed as ((predictedbiomass-measured biomass)measured biomass)lowast 100 [13]

Finally the developed equation for total tree biomasswas compared with several equations in similar managementunits but different geographical areasThe two sets of biomassvalues were subjected to a paired t test [14] to find ifdifferences occur in each biomass estimate comparison

3 Results

31 Preliminary Findings of the Dataset A total of 1090 treeswere measured for DBH in the twelve (12) plots 222 in AEZ 1308 in AEZ2 292 in AEZ 3 and 268 in AEZ 4 The values forDBH ranged from 1cm to 395cm with a mean of 1108 cm inAEZ1 1151 cm in AEZ 2 1007 cm in AEZ 2 and 1214 cm in

AEZ 4Height values ranged from60m to 248mwith ameanof 1167m in AEZ 4 1332m in AEZ 3 1403m in AEZ 2 and1142m in AEZ 1 Out of the 1090 trees measured for DBH 33trees were destructively sampled for biomass measurements

32 Percentage Contributions of Different Tree ComponentsBiomass The summary distribution of the total tree biomassand tree biomass components of the thirty-three destruc-tively sampled trees of different sizes recorded in the studyarea are as shown in Tables 4 and 5 The total tree biomass(TTB) for the 33 trees was 633589 kg distributed as followsstemtrunk (5689) branches (1411) foliage (667) androots (2233)Thus aboveground biomass (AGB) comprised7774while belowground biomass (BGB) was 2233Theseare the proportions of biomass available for specific useseg timber (stem biomass) fuel wood (branches biomass)mulchlivestock feedgreen manure (foliage biomass) andsoil organic carbon services (roots)

The stem comprises the largest percentage of the totaltree biomass (Table 5) while foliage has the least biomasscontribution and this is in agreement with similar studies[1 5 15] The 2233 proportion of BGB is close to the IPCCdefault value for BGB which is taken as 24 [16] The slightvariations in allocation among AEZ could be a justificationfor development of very specific allometric equations for eachof theAEZ For example the results indicated a slight increasein BGBAGB ratio with altitude rise from UM1 (0219) toUM4 (0293) Such information on component ratios amongG robusta and which is based on tree allometry variationsrequires further research and supports its conservation andusage

33 Illustrations of Biomass Estimation from Various Func-tions Various functions were plotted and the biomass esti-mates done for each function The goodness of fit in eachregression was illustrated by the coefficient of determination(R2 value) which explains how close the measured data are to

6 International Journal of Forestry Research

Table 6 Allometric equations for estimating various biomass using DBH

Function Equations MRE R2 SEEExponential TTB = 1091e0150DBH -2910 084 457Power TTB = 1811DBH1658 505 098 134Polynomial TTB = 0322DBBH2+793DBH-1926 015 093 133Linear TTB= 1800DBH - 7322 007 091 152Multiple TTB = 11356DBH ndash 8924HT + 0536(DBHlowastHT) + 1827 -016 093 140Exponential AGB=8474e0150DBH -2260 083 356Power AGB=1384DBH1665 32 098 099Linear AGB=1399DBH - 5696 002 092 112Polynomial AGB=0248DBH2 + 6243DBH ndash 1545 0002 094 099Multiple AGB=8641DBH ndash 69HT + 0424(DBHlowastHT) + 1453 006 090 198Exponential BGB = 2311e0151DBH -513 082 104Polynomial BGB = 0074DBH2+1688DBH ndash 3791 010 082 050Linear BGB = 4013DBH - 1624 -001 081 053Multiple BGB =2713DBH ndash 2028HT + 0111(DBHlowastHT) +379 010 082 051Power BGB = 0401DBH1642 342 093 051

the fitted regression line [14]These illustrations are shown inFigures 3 4 and 5

A comparison of functions for estimating TTB fromDBHillustrates that the exponential function overestimates DBHfor a tree of 35cm DBH Though the other three functionshave a near similar estimate the R2 values favor the powerfunction (R2 = 097) and the polynomial function (R2= 093)Though the linear function gives relatives good R2 valueforesters have disqualified linear relationships because theydo not illustrate the ideal relationship between predictorvariables and biomass or volume over a wide diameter sizedistribution [8 16]

Estimation of total tree biomass from height variedgreatly among functions making it difficult to select the idealfunction The R2 values were also lower compared to thoseof using DBH as a predictor variable The same trend wasnoted in estimating ABG from tree height Noting that heightmeasurement in forests is difficult and the fact that farmerssell trees while standing the use of tree height may increasetree biomass or volume estimation costs while not increasingaccuracy of estimates As such trials of height as a biomass-predictor variable were discarded in favor of DBH which iseasy to measure and can be measured with high levels ofaccuracy [6 8]

DBH gives a good estimate of AGB based on R2 valueswith 098 for the power function and 094 for the polynomialfunction Kuya [5] identified power functions as most idealfor estimating AGB in western Kenya while Henry et al[1] preferred polynomial functions It has been found thateither of these functions is ideal based on the diametersize distribution [8] Kuya [5] preferred power functionsbecause of the large DBH size distribution which disqualifiespolynomial functions which often have two turning points[14] and may not define the biomass-predictor relationshipover a wide range of diameter sizes In this case where Grobusta does not grow to large sizes in the study area either a

polynomial or a power function becomes ideal based on thiscriteria of choice

34 Choice of Equation Based on Standard Error of Estimateand Mean Residual Error Apart from the coefficient ofdetermination the standard error of estimate (SEE) and themean residual error (MRE) have been used in choice ofappropriate regression equations [14] The SEE is a measureof the accuracy of predictionsmadewith a regression line andthe lower the value the better the accuracy of an allometricequation [8] Zar [14] also explains the mean residual erroras another measure of the accuracy of a regression equationSince residuals are differences between the data points andthe regression line the mean residual error refers to the errorthat is not explained by the regression line

The choice of equation based on the three statistics isillustrated for the various biomass components in Table 6

Though linear functions had the least MRE for TTB andBGB their previously described limitations [8 14] disqual-ifies them The polynomial functions have very small MREvalues in all estimated biomass components of TTB (015kg)AGB (0002Kg) and BGB (01Kg) illustrating their appropri-ateness based on this second selection criteria Exponentialfunctions have large mean bias in all functions and thisfurther illustrates their inappropriateness in this selectionA bias of less than 5 of the total tree biomass is withinacceptable range [16 17] and would provide the farmers withthe real value of the tree In this case the polynomial functionis very accurate with very minimal bias within the range ofdiameter sizes tested

Based on the SEE the polynomial function gave thelowest values at 133 for TTB 099 for ABG and 05 forBGBThis compared well with the power function which had134 for TTB 099 for AGB and 051 for BGB In this thirdselection criteria the polynomial function again takes bestpreference

International Journal of Forestry Research 7

y = 18005x - 73223Rsup2 = 091

Linear Function

y = 10915e01504x

Rsup2 = 08361

Exponential function

y = 03223x 2 + 79347x - 19265 Rsup2 = 093

polynomial function

y = 1811x1658

Rsup2 = 09769

Power function

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0200400600800

10001200

Biom

ass (

Kg)

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

Figure 3 Comparison of functions for estimating total tree biomass from DBH

y = 30725e02672x

Rsup2 = 07813

Exponential Function

y = 29775x - 19625 Rsup2 = 07373

0 10 20 30

Tree Height (m)

Linear Function

y = 00332x32166

Rsup2 = 08693

Power Functiony = 03387x2 + 20641x - 14234

Rsup2 = 0741

0 10 20 30

Tree Height (m)

Polynomial Function

0

500

1000

1500

2000

2500

Biom

ass (

Kg)

10 20 300Tree Height (m) minus200

minus1000

100200300400500600

Biom

ass (

Kg)

minus200

0

200

400

600

800

Biom

ass (

Kg)

0200400600800

10001200

Biom

ass (

Kg)

10 20 300Tree Height (m)

Figure 4 A comparison of functions for estimating total tree biomass from tree height

Based on the statistics Table 7 shows the list of preferredequations for estimating the different tree biomass compo-nents Though all the preferred equations are polynomialfunctions it should be noted that the power functions werethe next best alternative and their application has alreadybeen illustrated for agroforestry species of western Kenya [5]The limitation of two turning points observed in polynomialfunctions [14] may not apply in the study area where Grobusta grows because the trees do not grow beyond the40cm DBH size that was used in this study It is howeverrecommended that such equations should not be appliedwhere trees of bigger sizes grow

Table 7 A list of selected allometric equations for estimatingbiomass components

Biomass component EquationsTotal Tree TTB = 0322DBBH2+793DBH-1926Above ground AGB=0248DBH2 + 6243DBH ndash 1545Below ground BGB = 0074DBH2+1688DBH ndash 3791Branches BRA = 0030DBH2 + 1574DBH ndash 4984Foliage F = 004DBH2 + 1949DBH ndash 3134

8 International Journal of Forestry Research

y = 1384x16658

Rsup2 = 09798

Power function

y = 13992x - 56966 Rsup2 = 09177

0 10 20 30 40

DBH (cm)

Linear function

y = 84746e01506x

Rsup2 = 0833

Exponential function

y = 0248x2 + 62437x - 15451 Rsup2 = 09374

0 10 20 30 40

DBH (cm)

Polynomial function

0

200

400

600

800

Biom

ass (

Kg)

10 20 30 400DBH (cm) minus100

0

100

200

300

400

500

Biom

ass (

Kg)

minus100

0

100

200

300

400

500

Biom

ass (

Kg)

0

100

200

300

400

500

Biom

ass (

Kg)

10 20 30 400DBH (cm)

Figure 5 A comparison of functions for estimating above ground tree biomass from DBH

Table 8 A validation of the equation with similar equations using the F values of the paired t-test

Author F calculated F critical Comments Discussion

Kuya [5] 15375557 18283There is nosignificantdifference

The Kuya equation was developed insimilar Agroforestry conditions but in a

different AEZs of Kenya

Henry [1] 0817302 18283There is nosignificantdifference

The equation was developed forAgroforestry trees of Western Kenya in a

different AEZ

Benedicto [19] 2070408 18408There is asignificantdifference

The equation was developed in Mexico Atotally different biome and may not be

applicable in the study area

Rurangwa [18] 1118687 18408There is nosignificantdifference

Rurangwa developed this equation inAgroforestry trees of Ruanda which is

within East Africa

Table 9 Average biomass values per hectare in AEZs

Component Average biomass (Kg) per hectareUM 1 UM 2 UM 3 UM 4

Foliage 922128 874343 724966 788837Branchesfoliage 1964818 1849623 1533623 1668739Rootsbelowground biomass 3109676 2927150 2427314 2640889Stemtrunk 7929378 7457484 6183147 6728175Total for tree 1392600 1310860 1086905 1182664

35 Validation of Developed Allometric Equations Validationof the equations based on the bias of the equation inestimating specific diameter sizes is illustrated in residualplots used to assist in validation which are shown in Figure 6

A second validation to compare biomass estimates fromthe preferred equation and that of similar studies showsthat the developed equation compares well with otherequations developed in agroforestry conditions of Kenya

[1 5] and Rwanda [18] but is not applicable in biomes farfrom the study area [19] This finding illustrates that theprocess of destructive sampling to develop new allomet-ric equations within a small geographical range may notenhance accuracy of estimates and an equation applicablein a similar land and tree management activity may as wellbe applicable in another one The results are illustrated inTable 8

International Journal of Forestry Research 9

0 10 20 30 40

DBH (cm)

Difference (Kg) Power function

0 10 20 30 40

DBH (cm)

Difference (Kg) Polynomial function

minus100

minus50

0

50

100Bi

omas

s res

idua

ls (k

g)

minus150

minus100

minus50

0

50

Biom

ass r

esid

uals

(kg)

Figure 6 Residual scatter plots of total tree biomass using polynomial and power function for TTB

Table 10 Total tree biomass and tree component biomass data of the 33 trees destructively sampled per every Agroecological Zone (AEZ)

AEZ Tree No DBH (cm) Height (m) Dry weights of biomass in kgStem Branches foliage AGB BGB TTB

UM4

1 52 655 1016 1625 522 1701 382 20832 15 36 155 0644 102 331 0801 4013 12 143 9369 1062 121 11641 3743 153844 132 127 7022 1108 1749 9879 2346 122255 225 167 16666 503 2292 23988 6314 303026 298 145 24752 8042 2127 34921 11955 468767V 18 60 165 033 0662 264 1461 4108V 137 145 11222 2661 1464 15347 3242 185899V 20 161 13487 315 1375 18012 5779 23791

UM3

10 120 1275 5901 688 1314 7903 324 1114311 154 137 1094 2475 2065 1548 5363 2084312 70 865 2038 50 75 3288 983 427113 56 865 1268 28 413 1961 594 255514 276 190 27053 9298 1797 38148 13037 5118515 277 192 30655 8325 160 4058 12708 5328816V 169 122 11803 4365 2239 18407 8603 270117V 98 91 3269 100 102 5289 1501 679418V 258 166 27516 6358 3326 3720 7495 44695

UM2

19 17 71 195 06 145 40 179 57920 87 98 2498 643 875 4016 786 480221 153 143 5883 385 1551 11284 2146 1343022 148 150 6963 3271 1046 1128 3399 1467923V 122 124 4063 1393 135 6806 1775 858124V 128 154 6294 1915 70 8909 2726 1163525 220 170 16471 3003 1109 20583 6836 2741926 298 212 2598 332 1089 30389 7934 3832327V 278 248 32763 439 871 38024 11475 49499

UM1

28 20 60 321 094 119 534 101 63529 89 99 2887 1025 1001 4913 590 550330V 45 91 1196 25 386 1832 360 219231 128 130 11466 3150 3122 17738 6522 242632 249 190 26284 3775 1857 31916 5650 3756633 204 115 12871 469 162 19181 3460 22641

10 International Journal of Forestry Research

Table 11 Allometric equations for estimating branch biomass using DBH

Function Equation MRE R2 SEEExponential BR = 4644e0069Dbh 1172 093 075Logarithmic BR = 1056ln(DBH) +1534 002 084 072Polynomial BR = 0077DBH2 + 3373DBH +0213 - 453 099 058Linear BR = 0941DBH+ 1324 003 096 073Power BR = 1901DBH0793 1159 099 073s

Table 12 Allometric equations for estimating foliage using DBH

Function Equation MRE R2 SEEExponential F = 4795e0045DBH 274 097 024Logarithmic F = 362ln(DBH) + 4020 002 084 022Polynomial F = -0031DBH2 + 1270DBH + 3235 -183 099 058Linear F = 0295DBH + 8452 0003 097 023Power F= 2213DBH0596 -237 098 023

Table 13 Allometric equations for estimating TTB using HT

Function Equation MRE R2 SEEExponential TTB = 3090e0266HT -3750 054 1010Logarithmic TTB = 3157ln(HT) ndash 5973 006 093 300Polynomial TTB = -00409HT2 + 1863HT + 1327 021 099 252Linear TTB = 2969HT- 1980 002 074 255Power TTB= 0401HT1642 -544 097 053

Table 14 Allometric equations for estimating AGB using HT

Function Equation MRE R2 SEEExponential AGB = 2454e0263HT -2437 054 744Logarithmic AGB = 2401ln(H) ndash 4526 0084 093 248Polynomial AGB= -0312HT2 + 1411HT- 9872 024 099 210Linear AGB= 2255HT-14850 002 070 212Power AGB= 0027HT3174 793 082 286

Table 15 Allometric equations for estimating BGB using HT

Function Equation MRE R2 SEEExponential BGB = 0631e0269HT -622 053 226Logarithmic BGB = 707ln(HT) - 1333 -004 093 079Polynomial BGB = -0067HT2 + 4781HTndash3258 015 1 071Linear BGB = 6009HTndash4345 010 064 2352Power BGB= 0006HT3241 584 080 3134

Table 16 Allometric equations for estimating TTB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential TTB= 2348e0006P -761 073 667Logarithmic TTB= 1077ln(P) - 3397 0002 072 285Polynomial TTB = -0000P2 + 111Pndash205 -402 I 252Linear TTB = 0829Pndash0929 006 090 158Power TTB= 0395P1125 215 098 268

International Journal of Forestry Research 11

Table 17 Allometric equations for estimating AGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential AGB = 1826e00006P -746 073 524Logarithmic AGB = 8222ln(P) ndash 2581 -688 072 231Polynomial AGB = -0000P2 + 0829Pndash1609 -29 1 185Linear AGB = 0630P + 0965 019 086 146Power AGB= 0310P1119 3837 099 152

Table 18 Allometric equations for estimating BGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential BGB = 495e00006P 134 073 -145Logarithmic BGB = 2424ln(P) ndash 7622 001 072 075Polynomial BGB = -0000P2 + 0255Pndash5495 -101 1 069Linear BGB = 0184P + 0575 007 078 075Power BGB= 0084P1125 306 099 075

Table 19 Generated TTB from developed equation using DBH

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM128 1295594 139 1474242 186 2336786 303 518241424 418944 1 6674 17 20251 298 50404221 6674 92 7725136 91 7593304 1 66741 6674 1 6674 188 2377058 44 221838444 2218384 1 6674 146 1592514 265 414892154 173205 135 140826 185 231676 1 667416 183976 1 6674 25 502 1 667410 8806 16 183976 16 183976 1 667410 8806 3 9282 194 2499618 16 18397613 132742 154 173205 108 9933456 18 221772128 1295594 215 294922 153 1714354 135 140826209 2817486 17 142064 128 1295594 1 667422 255016 122 1201862 162 1876246 148 162696219 241762 8 61912 209 2817486 175 212052 094 876 7150521 19 241762 16 18397689 7331824 13 132742 22 255016 15 1661714 371576 1 6674 78 5945736 185 23167612 520944 1 6674 52 3019696 14 149092165 193152 1 6674 45 2316 165 193152126 1264058 15 2958 45 2316 126 1264058153 1714354 1 6674 24 418944 153 171435413 132742 2 094 42 2025336 1 6674118 114083 97 8395216 51 2916984 13 13274214 371576 96 8259744 25 502 118 11408333 1192656 122 1201862 45 2316 145 1575415 2958 87 7073256 54 3227304 171 20440342 094 83 6564856 26 585784 1 66741 6674 109 1007766 1 6674 1 6674171 2044034 68 4762096 1 6674 18 221772171 2044034 69 4877184 9 74622 1 6674

12 International Journal of Forestry Research

Table 19 Continued

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM9 74622 29 841504 105 95052 124 1232814114 1080962 1 6674 46 2414344 114 1080962108 9933456 51 2916984 1 6674 108 993345611 102226 11 102226 1 6674 93 7857696105 95052 1 6674 1 6674 118 11408312 11712 12 11712 1 6674 156 17676627 4993 104 9363904 1 6674 7 4993122 1201862 52 3019696 7 4993 175 21205111 1036826 111 1036826 53 3123136 144 155835813 132742 61 3976864 13 446624 118 11408310 8806 1 6674 18 064104 10 8806128 1295594 128 1295594 1 6674 13 13274220 26248 68 4762096 1 6674 8 619121 6674 1 6674 1 6674 138 1457638104 9363904 1 6674 1 6674 114 108096214 149092 1 6674 98 8531416 154 17320516 183976 104 9363904 1 6674 84 6690864195 25203 62 4086856 1 6674 78 594573681 6315024 95 8125 28 755536 225 3174656 3437824 85 68176 49 2713744 1 667452 3019696 65 44212 42 2025336 156 176766210 8806 81 6315024 121 1186494 1 667413 132742 1 6674 87 7073256 1 6674169 2006238 1 6674 56 3437824 29 84150421 283926 82 6439576 1 6674 136 142464621 283926 57 3544176 15 16617 164 191302213 132742 1 6674 202 266711 1 667439 1741224 6 38676 297 5012242 1 6674173 2082122 1 6674 195 25203 17 2025116 183976 1 6674 23 329002 16 18397616 183976 1 6674 23 336616 187 235688621 283926 64 4309024 183 2276926 104 9363904187 2356886 48 2613216 12 11712 122 120186239 1741224 1 6674 54 3227304 13 132742132 1359538 1 6674 132 1359538 18 22177218 221772 1 6674 2 094 1 667458 3651256 15 2958 1 6674 1 6674

36 Biomass Stocks amongAgroecological Zones Based on theallometric equations the average TTB for G robusta treesgenerated in each of the AEZ studied is as shown in Table 9The TTB stock for each AEZ was 13 926 tonhaminus1 13109tonhaminus1 10869 tonhaminus1 and 11827 tonhaminus1 in UM1 UM2UM3 and UM4 respectively Variability of tree biomassbetween the four agroecological zones showed no significantdifference (p-value gt 005) implying that though there couldbe a slight difference in the allometry of the tree speciesamong AEZ the total biomass does not vary This alsoexplains that the management of G robusta trees in the

agricultural landscapes of the four AEZ does not differ andthe farmers can form a marketing unit despite their differentAEZ and their production quotas can be the same

The average biomass stock of 1243 tonha in the studycompares well with the findings of Albrecht [20] 2-22tonha Henry [1] 9ndash11tonha and Kuya [5] 16 tonhaall of which are for agricultural landscapes This findinggives a better glimpse of the tree component in agricul-tural landscapes and is a good guide for the develop-ment of carbon stock factors in agricultural landscapes[21] With this moderate stock the farmers are able to

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

4 International Journal of Forestry Research

Table 1 Biophysical and climatic conditions of Maragua subcounty (source [10])

Attribute Upper midland 1 (UM 1) Upper midland 2 (UM 2) Upper midland 3 (UM 3) Upper midland 4 (UM 4)Altitude range (m) 1730 - 2430 1500 ndash 1730 1340 ndash 1500 1060 - 1340Mean annual Rainfall (mm) 2200 15375 955 970Mean annual Temperature (∘C) 184∘C 193∘C 202 212

Table 2 Classification and description of soil in Maragua subcounty

AEZ Physiographic Lithology Soil description

UM 1 MV2Well drained very deep dark reddish to dark brown very friable and smeary clay loamto clay with thick acid humic topsoil in places shallow to moderately deep and rocky

Humic ANDOSOLS partly lithic phase

UM 2 RB1Well drained extremely deep dark reddish brown to dark brown friable and slightly

smeary clay with an acid humic topsoil Ando-humic NITISOLS with humicANDOSOLS

RB2 well drained extremely deep dusky red to dark reddish brown friable clay with an acidhumic topsoil humic NITISOL

UM 3 RB3

Well drained extremely deep dusky red to dark reddish brown friable clay with inclusionof well drained moderately deep dark red to dark reddish brown friable clay over rockpisoferric or petroferric materials Eutric NITISOLS with nito-chromic CAMBISOLSand chromic ACRISOLS and LUVISOLS partly lithic pisoferric or petroferric phase

UM 4 LB1 Well drained very deep dark red very friable clay Nito-rhodic FERRALSOLS

Table 3 Coordinates of data collection points for all the AEZs

Agroecological Zone Plot number Eastings (m) Nothings (m)

UM 41 305449791 99003082872 301575475 99087491653 297040133 9914658828

UM 31 290497054 98966631322 298551514 99030694503 289507887 9901526723

UM 21 281419488 99099827172 276445967 99045766373 268721854 9911103375

UM 11 263165408 98966631322 259196650 99185092813 256504015 9914786820

1) 2 le D lt 5 cm (Class 11) 5 le D lt 10 cm (Class 111) andDge 10 cm (Class IV) for easy of weighingTheir weights weretaken for green weight to the nearest 01 kg The heavier oneswere measured as individual billets while the lighter oneswere bundled together and weighed for their green weightAliquots were taken and labeled and their green weight wasrecorded to the nearest 001gm kept in bags and taken tothe laboratory for oven-dry (105∘C) weight measurementThe foliage was collected on to the tarpaulin sheet bundledinto gunny bags whose weights were known and weighedto the nearest 01kg Their green weights were calculated asthe difference between the gross weight and the weight ofthe empty gunny bags and recorded A sample of the foliagewas taken from the combined mass of the foliage weighedrecorded to the nearest 001gm and oven-dried (70∘C)

Excavation of the tree was done manually until all theroots were removedThe taproot was followed to its endpointand root length recorded Soil embedded in the stump jointsand on root surface was removed by use of a brush and waterThe roots were classified into size classes as (Class 1) 0 lt D lt2 cm (Class 11) 2 le D lt 10 cm and (Class 111) D ge10 cm forease of weighing Roots were weighed by size classes for greenweight and recorded An aliquot of each root size class wasextracted and weighed for green weight recorded taggedpackaged and taken to the laboratory to oven-dry at 105∘CIn all the cases the aliquots were left in the oven to dry andchanges in dry weight were monitored on a daily basis untilthey reached a constant weight

252 Biomass Measurement The aliquotrsquos green and oven-dry weights were used to get the dry-green weight ratiosThese were subsequently used to convert the green weight ofthe tree component (trunks branches foliage or roots) to dryweight which is the componentrsquos biomass The total above-ground (AGB) biomass was obtained by getting the sum ofthe biomass of the trunk branches and foliage Similarly thetotal belowground (BGB) biomass was obtained by summingup all the dry weights of all the root sections of that given treeFinally the total tree biomass (TTB) was obtained by addingup aboveground and belowground biomass Scatter plotsand function graphs were used in assessing the relationshipsbetween easilymeasurable variables of DBH andHT togetherwith a combination ofDBHandHT against total tree biomassand tree component biomass

253 Development of Biomass Equations Thirty-threedestructively sampled trees were used to develop the biomassestimation allometric equations The measured predictor

International Journal of Forestry Research 5

Table 4 Biomass partitions (Kg) of each component and total tree biomass of sampled trees for every AEZ

Zone Stem Branches Foliage AGB BGB TTBUM 1 55025 12984 8105 76114 16683 92795UM 2 101110 21845 8736 131691 37256 168947UM 3 120443 33289 14524 168256 53524 221784UM 4 83814 21313 10907 116084 33987 150061Total 360432 89431 42272 492545 141450 633589

Table 5 Percentage contribution to total tree biomass among tree components in the different AEZ

Zone Stem Branches Foliage AGB BGBUM 1 5930 1399 873 8202 1798UM 2 5985 1293 517 7795 2205UM 3 5431 1501 655 7586 2413UM 4 5585 1420 727 7736 2265Total 5689 1411 667 7774 2233

variables DBH height (Ht) and product of DBH and HT(DBHlowastHt) for each of the destructively sampled treeswere regressed to the dry weight (biomass) of the totaltree biomass (TTB) or component biomass [(AGB) (BGB)branches biomass (BR) and foliage biomass (F)]

Scatter plots were used in illustrating the relationshipsbetween total tree and tree component biomass with theeasily measurable variables To derive the equation for eachof the dependent variable (TTB AGB BGB BR and F) theregression functions (exponential linear polynomial andpower) were superimposed on the scatter plot graphs Theselection of the best fit equation was based on the loweststandard error of the estimate (SEE) which is the standarddeviation of the residuals the lowest residual mean error(RME) and the highest coefficient of determination (R2)

254 Validation of Developed Allometric Equations Themean differences between predicted and observed biomasswere used to test the suitability of the equation Simple linearregression analysis between observed and predicted values ofthe equations quantifies the tendency of residuals whereby R2and mean standard error (MSE) indicate the precision of theestimates Residual plots were also used to assist in the eval-uation of the equations Bias was computed as ((predictedbiomass-measured biomass)measured biomass)lowast 100 [13]

Finally the developed equation for total tree biomasswas compared with several equations in similar managementunits but different geographical areasThe two sets of biomassvalues were subjected to a paired t test [14] to find ifdifferences occur in each biomass estimate comparison

3 Results

31 Preliminary Findings of the Dataset A total of 1090 treeswere measured for DBH in the twelve (12) plots 222 in AEZ 1308 in AEZ2 292 in AEZ 3 and 268 in AEZ 4 The values forDBH ranged from 1cm to 395cm with a mean of 1108 cm inAEZ1 1151 cm in AEZ 2 1007 cm in AEZ 2 and 1214 cm in

AEZ 4Height values ranged from60m to 248mwith ameanof 1167m in AEZ 4 1332m in AEZ 3 1403m in AEZ 2 and1142m in AEZ 1 Out of the 1090 trees measured for DBH 33trees were destructively sampled for biomass measurements

32 Percentage Contributions of Different Tree ComponentsBiomass The summary distribution of the total tree biomassand tree biomass components of the thirty-three destruc-tively sampled trees of different sizes recorded in the studyarea are as shown in Tables 4 and 5 The total tree biomass(TTB) for the 33 trees was 633589 kg distributed as followsstemtrunk (5689) branches (1411) foliage (667) androots (2233)Thus aboveground biomass (AGB) comprised7774while belowground biomass (BGB) was 2233Theseare the proportions of biomass available for specific useseg timber (stem biomass) fuel wood (branches biomass)mulchlivestock feedgreen manure (foliage biomass) andsoil organic carbon services (roots)

The stem comprises the largest percentage of the totaltree biomass (Table 5) while foliage has the least biomasscontribution and this is in agreement with similar studies[1 5 15] The 2233 proportion of BGB is close to the IPCCdefault value for BGB which is taken as 24 [16] The slightvariations in allocation among AEZ could be a justificationfor development of very specific allometric equations for eachof theAEZ For example the results indicated a slight increasein BGBAGB ratio with altitude rise from UM1 (0219) toUM4 (0293) Such information on component ratios amongG robusta and which is based on tree allometry variationsrequires further research and supports its conservation andusage

33 Illustrations of Biomass Estimation from Various Func-tions Various functions were plotted and the biomass esti-mates done for each function The goodness of fit in eachregression was illustrated by the coefficient of determination(R2 value) which explains how close the measured data are to

6 International Journal of Forestry Research

Table 6 Allometric equations for estimating various biomass using DBH

Function Equations MRE R2 SEEExponential TTB = 1091e0150DBH -2910 084 457Power TTB = 1811DBH1658 505 098 134Polynomial TTB = 0322DBBH2+793DBH-1926 015 093 133Linear TTB= 1800DBH - 7322 007 091 152Multiple TTB = 11356DBH ndash 8924HT + 0536(DBHlowastHT) + 1827 -016 093 140Exponential AGB=8474e0150DBH -2260 083 356Power AGB=1384DBH1665 32 098 099Linear AGB=1399DBH - 5696 002 092 112Polynomial AGB=0248DBH2 + 6243DBH ndash 1545 0002 094 099Multiple AGB=8641DBH ndash 69HT + 0424(DBHlowastHT) + 1453 006 090 198Exponential BGB = 2311e0151DBH -513 082 104Polynomial BGB = 0074DBH2+1688DBH ndash 3791 010 082 050Linear BGB = 4013DBH - 1624 -001 081 053Multiple BGB =2713DBH ndash 2028HT + 0111(DBHlowastHT) +379 010 082 051Power BGB = 0401DBH1642 342 093 051

the fitted regression line [14]These illustrations are shown inFigures 3 4 and 5

A comparison of functions for estimating TTB fromDBHillustrates that the exponential function overestimates DBHfor a tree of 35cm DBH Though the other three functionshave a near similar estimate the R2 values favor the powerfunction (R2 = 097) and the polynomial function (R2= 093)Though the linear function gives relatives good R2 valueforesters have disqualified linear relationships because theydo not illustrate the ideal relationship between predictorvariables and biomass or volume over a wide diameter sizedistribution [8 16]

Estimation of total tree biomass from height variedgreatly among functions making it difficult to select the idealfunction The R2 values were also lower compared to thoseof using DBH as a predictor variable The same trend wasnoted in estimating ABG from tree height Noting that heightmeasurement in forests is difficult and the fact that farmerssell trees while standing the use of tree height may increasetree biomass or volume estimation costs while not increasingaccuracy of estimates As such trials of height as a biomass-predictor variable were discarded in favor of DBH which iseasy to measure and can be measured with high levels ofaccuracy [6 8]

DBH gives a good estimate of AGB based on R2 valueswith 098 for the power function and 094 for the polynomialfunction Kuya [5] identified power functions as most idealfor estimating AGB in western Kenya while Henry et al[1] preferred polynomial functions It has been found thateither of these functions is ideal based on the diametersize distribution [8] Kuya [5] preferred power functionsbecause of the large DBH size distribution which disqualifiespolynomial functions which often have two turning points[14] and may not define the biomass-predictor relationshipover a wide range of diameter sizes In this case where Grobusta does not grow to large sizes in the study area either a

polynomial or a power function becomes ideal based on thiscriteria of choice

34 Choice of Equation Based on Standard Error of Estimateand Mean Residual Error Apart from the coefficient ofdetermination the standard error of estimate (SEE) and themean residual error (MRE) have been used in choice ofappropriate regression equations [14] The SEE is a measureof the accuracy of predictionsmadewith a regression line andthe lower the value the better the accuracy of an allometricequation [8] Zar [14] also explains the mean residual erroras another measure of the accuracy of a regression equationSince residuals are differences between the data points andthe regression line the mean residual error refers to the errorthat is not explained by the regression line

The choice of equation based on the three statistics isillustrated for the various biomass components in Table 6

Though linear functions had the least MRE for TTB andBGB their previously described limitations [8 14] disqual-ifies them The polynomial functions have very small MREvalues in all estimated biomass components of TTB (015kg)AGB (0002Kg) and BGB (01Kg) illustrating their appropri-ateness based on this second selection criteria Exponentialfunctions have large mean bias in all functions and thisfurther illustrates their inappropriateness in this selectionA bias of less than 5 of the total tree biomass is withinacceptable range [16 17] and would provide the farmers withthe real value of the tree In this case the polynomial functionis very accurate with very minimal bias within the range ofdiameter sizes tested

Based on the SEE the polynomial function gave thelowest values at 133 for TTB 099 for ABG and 05 forBGBThis compared well with the power function which had134 for TTB 099 for AGB and 051 for BGB In this thirdselection criteria the polynomial function again takes bestpreference

International Journal of Forestry Research 7

y = 18005x - 73223Rsup2 = 091

Linear Function

y = 10915e01504x

Rsup2 = 08361

Exponential function

y = 03223x 2 + 79347x - 19265 Rsup2 = 093

polynomial function

y = 1811x1658

Rsup2 = 09769

Power function

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0200400600800

10001200

Biom

ass (

Kg)

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

Figure 3 Comparison of functions for estimating total tree biomass from DBH

y = 30725e02672x

Rsup2 = 07813

Exponential Function

y = 29775x - 19625 Rsup2 = 07373

0 10 20 30

Tree Height (m)

Linear Function

y = 00332x32166

Rsup2 = 08693

Power Functiony = 03387x2 + 20641x - 14234

Rsup2 = 0741

0 10 20 30

Tree Height (m)

Polynomial Function

0

500

1000

1500

2000

2500

Biom

ass (

Kg)

10 20 300Tree Height (m) minus200

minus1000

100200300400500600

Biom

ass (

Kg)

minus200

0

200

400

600

800

Biom

ass (

Kg)

0200400600800

10001200

Biom

ass (

Kg)

10 20 300Tree Height (m)

Figure 4 A comparison of functions for estimating total tree biomass from tree height

Based on the statistics Table 7 shows the list of preferredequations for estimating the different tree biomass compo-nents Though all the preferred equations are polynomialfunctions it should be noted that the power functions werethe next best alternative and their application has alreadybeen illustrated for agroforestry species of western Kenya [5]The limitation of two turning points observed in polynomialfunctions [14] may not apply in the study area where Grobusta grows because the trees do not grow beyond the40cm DBH size that was used in this study It is howeverrecommended that such equations should not be appliedwhere trees of bigger sizes grow

Table 7 A list of selected allometric equations for estimatingbiomass components

Biomass component EquationsTotal Tree TTB = 0322DBBH2+793DBH-1926Above ground AGB=0248DBH2 + 6243DBH ndash 1545Below ground BGB = 0074DBH2+1688DBH ndash 3791Branches BRA = 0030DBH2 + 1574DBH ndash 4984Foliage F = 004DBH2 + 1949DBH ndash 3134

8 International Journal of Forestry Research

y = 1384x16658

Rsup2 = 09798

Power function

y = 13992x - 56966 Rsup2 = 09177

0 10 20 30 40

DBH (cm)

Linear function

y = 84746e01506x

Rsup2 = 0833

Exponential function

y = 0248x2 + 62437x - 15451 Rsup2 = 09374

0 10 20 30 40

DBH (cm)

Polynomial function

0

200

400

600

800

Biom

ass (

Kg)

10 20 30 400DBH (cm) minus100

0

100

200

300

400

500

Biom

ass (

Kg)

minus100

0

100

200

300

400

500

Biom

ass (

Kg)

0

100

200

300

400

500

Biom

ass (

Kg)

10 20 30 400DBH (cm)

Figure 5 A comparison of functions for estimating above ground tree biomass from DBH

Table 8 A validation of the equation with similar equations using the F values of the paired t-test

Author F calculated F critical Comments Discussion

Kuya [5] 15375557 18283There is nosignificantdifference

The Kuya equation was developed insimilar Agroforestry conditions but in a

different AEZs of Kenya

Henry [1] 0817302 18283There is nosignificantdifference

The equation was developed forAgroforestry trees of Western Kenya in a

different AEZ

Benedicto [19] 2070408 18408There is asignificantdifference

The equation was developed in Mexico Atotally different biome and may not be

applicable in the study area

Rurangwa [18] 1118687 18408There is nosignificantdifference

Rurangwa developed this equation inAgroforestry trees of Ruanda which is

within East Africa

Table 9 Average biomass values per hectare in AEZs

Component Average biomass (Kg) per hectareUM 1 UM 2 UM 3 UM 4

Foliage 922128 874343 724966 788837Branchesfoliage 1964818 1849623 1533623 1668739Rootsbelowground biomass 3109676 2927150 2427314 2640889Stemtrunk 7929378 7457484 6183147 6728175Total for tree 1392600 1310860 1086905 1182664

35 Validation of Developed Allometric Equations Validationof the equations based on the bias of the equation inestimating specific diameter sizes is illustrated in residualplots used to assist in validation which are shown in Figure 6

A second validation to compare biomass estimates fromthe preferred equation and that of similar studies showsthat the developed equation compares well with otherequations developed in agroforestry conditions of Kenya

[1 5] and Rwanda [18] but is not applicable in biomes farfrom the study area [19] This finding illustrates that theprocess of destructive sampling to develop new allomet-ric equations within a small geographical range may notenhance accuracy of estimates and an equation applicablein a similar land and tree management activity may as wellbe applicable in another one The results are illustrated inTable 8

International Journal of Forestry Research 9

0 10 20 30 40

DBH (cm)

Difference (Kg) Power function

0 10 20 30 40

DBH (cm)

Difference (Kg) Polynomial function

minus100

minus50

0

50

100Bi

omas

s res

idua

ls (k

g)

minus150

minus100

minus50

0

50

Biom

ass r

esid

uals

(kg)

Figure 6 Residual scatter plots of total tree biomass using polynomial and power function for TTB

Table 10 Total tree biomass and tree component biomass data of the 33 trees destructively sampled per every Agroecological Zone (AEZ)

AEZ Tree No DBH (cm) Height (m) Dry weights of biomass in kgStem Branches foliage AGB BGB TTB

UM4

1 52 655 1016 1625 522 1701 382 20832 15 36 155 0644 102 331 0801 4013 12 143 9369 1062 121 11641 3743 153844 132 127 7022 1108 1749 9879 2346 122255 225 167 16666 503 2292 23988 6314 303026 298 145 24752 8042 2127 34921 11955 468767V 18 60 165 033 0662 264 1461 4108V 137 145 11222 2661 1464 15347 3242 185899V 20 161 13487 315 1375 18012 5779 23791

UM3

10 120 1275 5901 688 1314 7903 324 1114311 154 137 1094 2475 2065 1548 5363 2084312 70 865 2038 50 75 3288 983 427113 56 865 1268 28 413 1961 594 255514 276 190 27053 9298 1797 38148 13037 5118515 277 192 30655 8325 160 4058 12708 5328816V 169 122 11803 4365 2239 18407 8603 270117V 98 91 3269 100 102 5289 1501 679418V 258 166 27516 6358 3326 3720 7495 44695

UM2

19 17 71 195 06 145 40 179 57920 87 98 2498 643 875 4016 786 480221 153 143 5883 385 1551 11284 2146 1343022 148 150 6963 3271 1046 1128 3399 1467923V 122 124 4063 1393 135 6806 1775 858124V 128 154 6294 1915 70 8909 2726 1163525 220 170 16471 3003 1109 20583 6836 2741926 298 212 2598 332 1089 30389 7934 3832327V 278 248 32763 439 871 38024 11475 49499

UM1

28 20 60 321 094 119 534 101 63529 89 99 2887 1025 1001 4913 590 550330V 45 91 1196 25 386 1832 360 219231 128 130 11466 3150 3122 17738 6522 242632 249 190 26284 3775 1857 31916 5650 3756633 204 115 12871 469 162 19181 3460 22641

10 International Journal of Forestry Research

Table 11 Allometric equations for estimating branch biomass using DBH

Function Equation MRE R2 SEEExponential BR = 4644e0069Dbh 1172 093 075Logarithmic BR = 1056ln(DBH) +1534 002 084 072Polynomial BR = 0077DBH2 + 3373DBH +0213 - 453 099 058Linear BR = 0941DBH+ 1324 003 096 073Power BR = 1901DBH0793 1159 099 073s

Table 12 Allometric equations for estimating foliage using DBH

Function Equation MRE R2 SEEExponential F = 4795e0045DBH 274 097 024Logarithmic F = 362ln(DBH) + 4020 002 084 022Polynomial F = -0031DBH2 + 1270DBH + 3235 -183 099 058Linear F = 0295DBH + 8452 0003 097 023Power F= 2213DBH0596 -237 098 023

Table 13 Allometric equations for estimating TTB using HT

Function Equation MRE R2 SEEExponential TTB = 3090e0266HT -3750 054 1010Logarithmic TTB = 3157ln(HT) ndash 5973 006 093 300Polynomial TTB = -00409HT2 + 1863HT + 1327 021 099 252Linear TTB = 2969HT- 1980 002 074 255Power TTB= 0401HT1642 -544 097 053

Table 14 Allometric equations for estimating AGB using HT

Function Equation MRE R2 SEEExponential AGB = 2454e0263HT -2437 054 744Logarithmic AGB = 2401ln(H) ndash 4526 0084 093 248Polynomial AGB= -0312HT2 + 1411HT- 9872 024 099 210Linear AGB= 2255HT-14850 002 070 212Power AGB= 0027HT3174 793 082 286

Table 15 Allometric equations for estimating BGB using HT

Function Equation MRE R2 SEEExponential BGB = 0631e0269HT -622 053 226Logarithmic BGB = 707ln(HT) - 1333 -004 093 079Polynomial BGB = -0067HT2 + 4781HTndash3258 015 1 071Linear BGB = 6009HTndash4345 010 064 2352Power BGB= 0006HT3241 584 080 3134

Table 16 Allometric equations for estimating TTB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential TTB= 2348e0006P -761 073 667Logarithmic TTB= 1077ln(P) - 3397 0002 072 285Polynomial TTB = -0000P2 + 111Pndash205 -402 I 252Linear TTB = 0829Pndash0929 006 090 158Power TTB= 0395P1125 215 098 268

International Journal of Forestry Research 11

Table 17 Allometric equations for estimating AGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential AGB = 1826e00006P -746 073 524Logarithmic AGB = 8222ln(P) ndash 2581 -688 072 231Polynomial AGB = -0000P2 + 0829Pndash1609 -29 1 185Linear AGB = 0630P + 0965 019 086 146Power AGB= 0310P1119 3837 099 152

Table 18 Allometric equations for estimating BGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential BGB = 495e00006P 134 073 -145Logarithmic BGB = 2424ln(P) ndash 7622 001 072 075Polynomial BGB = -0000P2 + 0255Pndash5495 -101 1 069Linear BGB = 0184P + 0575 007 078 075Power BGB= 0084P1125 306 099 075

Table 19 Generated TTB from developed equation using DBH

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM128 1295594 139 1474242 186 2336786 303 518241424 418944 1 6674 17 20251 298 50404221 6674 92 7725136 91 7593304 1 66741 6674 1 6674 188 2377058 44 221838444 2218384 1 6674 146 1592514 265 414892154 173205 135 140826 185 231676 1 667416 183976 1 6674 25 502 1 667410 8806 16 183976 16 183976 1 667410 8806 3 9282 194 2499618 16 18397613 132742 154 173205 108 9933456 18 221772128 1295594 215 294922 153 1714354 135 140826209 2817486 17 142064 128 1295594 1 667422 255016 122 1201862 162 1876246 148 162696219 241762 8 61912 209 2817486 175 212052 094 876 7150521 19 241762 16 18397689 7331824 13 132742 22 255016 15 1661714 371576 1 6674 78 5945736 185 23167612 520944 1 6674 52 3019696 14 149092165 193152 1 6674 45 2316 165 193152126 1264058 15 2958 45 2316 126 1264058153 1714354 1 6674 24 418944 153 171435413 132742 2 094 42 2025336 1 6674118 114083 97 8395216 51 2916984 13 13274214 371576 96 8259744 25 502 118 11408333 1192656 122 1201862 45 2316 145 1575415 2958 87 7073256 54 3227304 171 20440342 094 83 6564856 26 585784 1 66741 6674 109 1007766 1 6674 1 6674171 2044034 68 4762096 1 6674 18 221772171 2044034 69 4877184 9 74622 1 6674

12 International Journal of Forestry Research

Table 19 Continued

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM9 74622 29 841504 105 95052 124 1232814114 1080962 1 6674 46 2414344 114 1080962108 9933456 51 2916984 1 6674 108 993345611 102226 11 102226 1 6674 93 7857696105 95052 1 6674 1 6674 118 11408312 11712 12 11712 1 6674 156 17676627 4993 104 9363904 1 6674 7 4993122 1201862 52 3019696 7 4993 175 21205111 1036826 111 1036826 53 3123136 144 155835813 132742 61 3976864 13 446624 118 11408310 8806 1 6674 18 064104 10 8806128 1295594 128 1295594 1 6674 13 13274220 26248 68 4762096 1 6674 8 619121 6674 1 6674 1 6674 138 1457638104 9363904 1 6674 1 6674 114 108096214 149092 1 6674 98 8531416 154 17320516 183976 104 9363904 1 6674 84 6690864195 25203 62 4086856 1 6674 78 594573681 6315024 95 8125 28 755536 225 3174656 3437824 85 68176 49 2713744 1 667452 3019696 65 44212 42 2025336 156 176766210 8806 81 6315024 121 1186494 1 667413 132742 1 6674 87 7073256 1 6674169 2006238 1 6674 56 3437824 29 84150421 283926 82 6439576 1 6674 136 142464621 283926 57 3544176 15 16617 164 191302213 132742 1 6674 202 266711 1 667439 1741224 6 38676 297 5012242 1 6674173 2082122 1 6674 195 25203 17 2025116 183976 1 6674 23 329002 16 18397616 183976 1 6674 23 336616 187 235688621 283926 64 4309024 183 2276926 104 9363904187 2356886 48 2613216 12 11712 122 120186239 1741224 1 6674 54 3227304 13 132742132 1359538 1 6674 132 1359538 18 22177218 221772 1 6674 2 094 1 667458 3651256 15 2958 1 6674 1 6674

36 Biomass Stocks amongAgroecological Zones Based on theallometric equations the average TTB for G robusta treesgenerated in each of the AEZ studied is as shown in Table 9The TTB stock for each AEZ was 13 926 tonhaminus1 13109tonhaminus1 10869 tonhaminus1 and 11827 tonhaminus1 in UM1 UM2UM3 and UM4 respectively Variability of tree biomassbetween the four agroecological zones showed no significantdifference (p-value gt 005) implying that though there couldbe a slight difference in the allometry of the tree speciesamong AEZ the total biomass does not vary This alsoexplains that the management of G robusta trees in the

agricultural landscapes of the four AEZ does not differ andthe farmers can form a marketing unit despite their differentAEZ and their production quotas can be the same

The average biomass stock of 1243 tonha in the studycompares well with the findings of Albrecht [20] 2-22tonha Henry [1] 9ndash11tonha and Kuya [5] 16 tonhaall of which are for agricultural landscapes This findinggives a better glimpse of the tree component in agricul-tural landscapes and is a good guide for the develop-ment of carbon stock factors in agricultural landscapes[21] With this moderate stock the farmers are able to

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

International Journal of Forestry Research 5

Table 4 Biomass partitions (Kg) of each component and total tree biomass of sampled trees for every AEZ

Zone Stem Branches Foliage AGB BGB TTBUM 1 55025 12984 8105 76114 16683 92795UM 2 101110 21845 8736 131691 37256 168947UM 3 120443 33289 14524 168256 53524 221784UM 4 83814 21313 10907 116084 33987 150061Total 360432 89431 42272 492545 141450 633589

Table 5 Percentage contribution to total tree biomass among tree components in the different AEZ

Zone Stem Branches Foliage AGB BGBUM 1 5930 1399 873 8202 1798UM 2 5985 1293 517 7795 2205UM 3 5431 1501 655 7586 2413UM 4 5585 1420 727 7736 2265Total 5689 1411 667 7774 2233

variables DBH height (Ht) and product of DBH and HT(DBHlowastHt) for each of the destructively sampled treeswere regressed to the dry weight (biomass) of the totaltree biomass (TTB) or component biomass [(AGB) (BGB)branches biomass (BR) and foliage biomass (F)]

Scatter plots were used in illustrating the relationshipsbetween total tree and tree component biomass with theeasily measurable variables To derive the equation for eachof the dependent variable (TTB AGB BGB BR and F) theregression functions (exponential linear polynomial andpower) were superimposed on the scatter plot graphs Theselection of the best fit equation was based on the loweststandard error of the estimate (SEE) which is the standarddeviation of the residuals the lowest residual mean error(RME) and the highest coefficient of determination (R2)

254 Validation of Developed Allometric Equations Themean differences between predicted and observed biomasswere used to test the suitability of the equation Simple linearregression analysis between observed and predicted values ofthe equations quantifies the tendency of residuals whereby R2and mean standard error (MSE) indicate the precision of theestimates Residual plots were also used to assist in the eval-uation of the equations Bias was computed as ((predictedbiomass-measured biomass)measured biomass)lowast 100 [13]

Finally the developed equation for total tree biomasswas compared with several equations in similar managementunits but different geographical areasThe two sets of biomassvalues were subjected to a paired t test [14] to find ifdifferences occur in each biomass estimate comparison

3 Results

31 Preliminary Findings of the Dataset A total of 1090 treeswere measured for DBH in the twelve (12) plots 222 in AEZ 1308 in AEZ2 292 in AEZ 3 and 268 in AEZ 4 The values forDBH ranged from 1cm to 395cm with a mean of 1108 cm inAEZ1 1151 cm in AEZ 2 1007 cm in AEZ 2 and 1214 cm in

AEZ 4Height values ranged from60m to 248mwith ameanof 1167m in AEZ 4 1332m in AEZ 3 1403m in AEZ 2 and1142m in AEZ 1 Out of the 1090 trees measured for DBH 33trees were destructively sampled for biomass measurements

32 Percentage Contributions of Different Tree ComponentsBiomass The summary distribution of the total tree biomassand tree biomass components of the thirty-three destruc-tively sampled trees of different sizes recorded in the studyarea are as shown in Tables 4 and 5 The total tree biomass(TTB) for the 33 trees was 633589 kg distributed as followsstemtrunk (5689) branches (1411) foliage (667) androots (2233)Thus aboveground biomass (AGB) comprised7774while belowground biomass (BGB) was 2233Theseare the proportions of biomass available for specific useseg timber (stem biomass) fuel wood (branches biomass)mulchlivestock feedgreen manure (foliage biomass) andsoil organic carbon services (roots)

The stem comprises the largest percentage of the totaltree biomass (Table 5) while foliage has the least biomasscontribution and this is in agreement with similar studies[1 5 15] The 2233 proportion of BGB is close to the IPCCdefault value for BGB which is taken as 24 [16] The slightvariations in allocation among AEZ could be a justificationfor development of very specific allometric equations for eachof theAEZ For example the results indicated a slight increasein BGBAGB ratio with altitude rise from UM1 (0219) toUM4 (0293) Such information on component ratios amongG robusta and which is based on tree allometry variationsrequires further research and supports its conservation andusage

33 Illustrations of Biomass Estimation from Various Func-tions Various functions were plotted and the biomass esti-mates done for each function The goodness of fit in eachregression was illustrated by the coefficient of determination(R2 value) which explains how close the measured data are to

6 International Journal of Forestry Research

Table 6 Allometric equations for estimating various biomass using DBH

Function Equations MRE R2 SEEExponential TTB = 1091e0150DBH -2910 084 457Power TTB = 1811DBH1658 505 098 134Polynomial TTB = 0322DBBH2+793DBH-1926 015 093 133Linear TTB= 1800DBH - 7322 007 091 152Multiple TTB = 11356DBH ndash 8924HT + 0536(DBHlowastHT) + 1827 -016 093 140Exponential AGB=8474e0150DBH -2260 083 356Power AGB=1384DBH1665 32 098 099Linear AGB=1399DBH - 5696 002 092 112Polynomial AGB=0248DBH2 + 6243DBH ndash 1545 0002 094 099Multiple AGB=8641DBH ndash 69HT + 0424(DBHlowastHT) + 1453 006 090 198Exponential BGB = 2311e0151DBH -513 082 104Polynomial BGB = 0074DBH2+1688DBH ndash 3791 010 082 050Linear BGB = 4013DBH - 1624 -001 081 053Multiple BGB =2713DBH ndash 2028HT + 0111(DBHlowastHT) +379 010 082 051Power BGB = 0401DBH1642 342 093 051

the fitted regression line [14]These illustrations are shown inFigures 3 4 and 5

A comparison of functions for estimating TTB fromDBHillustrates that the exponential function overestimates DBHfor a tree of 35cm DBH Though the other three functionshave a near similar estimate the R2 values favor the powerfunction (R2 = 097) and the polynomial function (R2= 093)Though the linear function gives relatives good R2 valueforesters have disqualified linear relationships because theydo not illustrate the ideal relationship between predictorvariables and biomass or volume over a wide diameter sizedistribution [8 16]

Estimation of total tree biomass from height variedgreatly among functions making it difficult to select the idealfunction The R2 values were also lower compared to thoseof using DBH as a predictor variable The same trend wasnoted in estimating ABG from tree height Noting that heightmeasurement in forests is difficult and the fact that farmerssell trees while standing the use of tree height may increasetree biomass or volume estimation costs while not increasingaccuracy of estimates As such trials of height as a biomass-predictor variable were discarded in favor of DBH which iseasy to measure and can be measured with high levels ofaccuracy [6 8]

DBH gives a good estimate of AGB based on R2 valueswith 098 for the power function and 094 for the polynomialfunction Kuya [5] identified power functions as most idealfor estimating AGB in western Kenya while Henry et al[1] preferred polynomial functions It has been found thateither of these functions is ideal based on the diametersize distribution [8] Kuya [5] preferred power functionsbecause of the large DBH size distribution which disqualifiespolynomial functions which often have two turning points[14] and may not define the biomass-predictor relationshipover a wide range of diameter sizes In this case where Grobusta does not grow to large sizes in the study area either a

polynomial or a power function becomes ideal based on thiscriteria of choice

34 Choice of Equation Based on Standard Error of Estimateand Mean Residual Error Apart from the coefficient ofdetermination the standard error of estimate (SEE) and themean residual error (MRE) have been used in choice ofappropriate regression equations [14] The SEE is a measureof the accuracy of predictionsmadewith a regression line andthe lower the value the better the accuracy of an allometricequation [8] Zar [14] also explains the mean residual erroras another measure of the accuracy of a regression equationSince residuals are differences between the data points andthe regression line the mean residual error refers to the errorthat is not explained by the regression line

The choice of equation based on the three statistics isillustrated for the various biomass components in Table 6

Though linear functions had the least MRE for TTB andBGB their previously described limitations [8 14] disqual-ifies them The polynomial functions have very small MREvalues in all estimated biomass components of TTB (015kg)AGB (0002Kg) and BGB (01Kg) illustrating their appropri-ateness based on this second selection criteria Exponentialfunctions have large mean bias in all functions and thisfurther illustrates their inappropriateness in this selectionA bias of less than 5 of the total tree biomass is withinacceptable range [16 17] and would provide the farmers withthe real value of the tree In this case the polynomial functionis very accurate with very minimal bias within the range ofdiameter sizes tested

Based on the SEE the polynomial function gave thelowest values at 133 for TTB 099 for ABG and 05 forBGBThis compared well with the power function which had134 for TTB 099 for AGB and 051 for BGB In this thirdselection criteria the polynomial function again takes bestpreference

International Journal of Forestry Research 7

y = 18005x - 73223Rsup2 = 091

Linear Function

y = 10915e01504x

Rsup2 = 08361

Exponential function

y = 03223x 2 + 79347x - 19265 Rsup2 = 093

polynomial function

y = 1811x1658

Rsup2 = 09769

Power function

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0200400600800

10001200

Biom

ass (

Kg)

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

Figure 3 Comparison of functions for estimating total tree biomass from DBH

y = 30725e02672x

Rsup2 = 07813

Exponential Function

y = 29775x - 19625 Rsup2 = 07373

0 10 20 30

Tree Height (m)

Linear Function

y = 00332x32166

Rsup2 = 08693

Power Functiony = 03387x2 + 20641x - 14234

Rsup2 = 0741

0 10 20 30

Tree Height (m)

Polynomial Function

0

500

1000

1500

2000

2500

Biom

ass (

Kg)

10 20 300Tree Height (m) minus200

minus1000

100200300400500600

Biom

ass (

Kg)

minus200

0

200

400

600

800

Biom

ass (

Kg)

0200400600800

10001200

Biom

ass (

Kg)

10 20 300Tree Height (m)

Figure 4 A comparison of functions for estimating total tree biomass from tree height

Based on the statistics Table 7 shows the list of preferredequations for estimating the different tree biomass compo-nents Though all the preferred equations are polynomialfunctions it should be noted that the power functions werethe next best alternative and their application has alreadybeen illustrated for agroforestry species of western Kenya [5]The limitation of two turning points observed in polynomialfunctions [14] may not apply in the study area where Grobusta grows because the trees do not grow beyond the40cm DBH size that was used in this study It is howeverrecommended that such equations should not be appliedwhere trees of bigger sizes grow

Table 7 A list of selected allometric equations for estimatingbiomass components

Biomass component EquationsTotal Tree TTB = 0322DBBH2+793DBH-1926Above ground AGB=0248DBH2 + 6243DBH ndash 1545Below ground BGB = 0074DBH2+1688DBH ndash 3791Branches BRA = 0030DBH2 + 1574DBH ndash 4984Foliage F = 004DBH2 + 1949DBH ndash 3134

8 International Journal of Forestry Research

y = 1384x16658

Rsup2 = 09798

Power function

y = 13992x - 56966 Rsup2 = 09177

0 10 20 30 40

DBH (cm)

Linear function

y = 84746e01506x

Rsup2 = 0833

Exponential function

y = 0248x2 + 62437x - 15451 Rsup2 = 09374

0 10 20 30 40

DBH (cm)

Polynomial function

0

200

400

600

800

Biom

ass (

Kg)

10 20 30 400DBH (cm) minus100

0

100

200

300

400

500

Biom

ass (

Kg)

minus100

0

100

200

300

400

500

Biom

ass (

Kg)

0

100

200

300

400

500

Biom

ass (

Kg)

10 20 30 400DBH (cm)

Figure 5 A comparison of functions for estimating above ground tree biomass from DBH

Table 8 A validation of the equation with similar equations using the F values of the paired t-test

Author F calculated F critical Comments Discussion

Kuya [5] 15375557 18283There is nosignificantdifference

The Kuya equation was developed insimilar Agroforestry conditions but in a

different AEZs of Kenya

Henry [1] 0817302 18283There is nosignificantdifference

The equation was developed forAgroforestry trees of Western Kenya in a

different AEZ

Benedicto [19] 2070408 18408There is asignificantdifference

The equation was developed in Mexico Atotally different biome and may not be

applicable in the study area

Rurangwa [18] 1118687 18408There is nosignificantdifference

Rurangwa developed this equation inAgroforestry trees of Ruanda which is

within East Africa

Table 9 Average biomass values per hectare in AEZs

Component Average biomass (Kg) per hectareUM 1 UM 2 UM 3 UM 4

Foliage 922128 874343 724966 788837Branchesfoliage 1964818 1849623 1533623 1668739Rootsbelowground biomass 3109676 2927150 2427314 2640889Stemtrunk 7929378 7457484 6183147 6728175Total for tree 1392600 1310860 1086905 1182664

35 Validation of Developed Allometric Equations Validationof the equations based on the bias of the equation inestimating specific diameter sizes is illustrated in residualplots used to assist in validation which are shown in Figure 6

A second validation to compare biomass estimates fromthe preferred equation and that of similar studies showsthat the developed equation compares well with otherequations developed in agroforestry conditions of Kenya

[1 5] and Rwanda [18] but is not applicable in biomes farfrom the study area [19] This finding illustrates that theprocess of destructive sampling to develop new allomet-ric equations within a small geographical range may notenhance accuracy of estimates and an equation applicablein a similar land and tree management activity may as wellbe applicable in another one The results are illustrated inTable 8

International Journal of Forestry Research 9

0 10 20 30 40

DBH (cm)

Difference (Kg) Power function

0 10 20 30 40

DBH (cm)

Difference (Kg) Polynomial function

minus100

minus50

0

50

100Bi

omas

s res

idua

ls (k

g)

minus150

minus100

minus50

0

50

Biom

ass r

esid

uals

(kg)

Figure 6 Residual scatter plots of total tree biomass using polynomial and power function for TTB

Table 10 Total tree biomass and tree component biomass data of the 33 trees destructively sampled per every Agroecological Zone (AEZ)

AEZ Tree No DBH (cm) Height (m) Dry weights of biomass in kgStem Branches foliage AGB BGB TTB

UM4

1 52 655 1016 1625 522 1701 382 20832 15 36 155 0644 102 331 0801 4013 12 143 9369 1062 121 11641 3743 153844 132 127 7022 1108 1749 9879 2346 122255 225 167 16666 503 2292 23988 6314 303026 298 145 24752 8042 2127 34921 11955 468767V 18 60 165 033 0662 264 1461 4108V 137 145 11222 2661 1464 15347 3242 185899V 20 161 13487 315 1375 18012 5779 23791

UM3

10 120 1275 5901 688 1314 7903 324 1114311 154 137 1094 2475 2065 1548 5363 2084312 70 865 2038 50 75 3288 983 427113 56 865 1268 28 413 1961 594 255514 276 190 27053 9298 1797 38148 13037 5118515 277 192 30655 8325 160 4058 12708 5328816V 169 122 11803 4365 2239 18407 8603 270117V 98 91 3269 100 102 5289 1501 679418V 258 166 27516 6358 3326 3720 7495 44695

UM2

19 17 71 195 06 145 40 179 57920 87 98 2498 643 875 4016 786 480221 153 143 5883 385 1551 11284 2146 1343022 148 150 6963 3271 1046 1128 3399 1467923V 122 124 4063 1393 135 6806 1775 858124V 128 154 6294 1915 70 8909 2726 1163525 220 170 16471 3003 1109 20583 6836 2741926 298 212 2598 332 1089 30389 7934 3832327V 278 248 32763 439 871 38024 11475 49499

UM1

28 20 60 321 094 119 534 101 63529 89 99 2887 1025 1001 4913 590 550330V 45 91 1196 25 386 1832 360 219231 128 130 11466 3150 3122 17738 6522 242632 249 190 26284 3775 1857 31916 5650 3756633 204 115 12871 469 162 19181 3460 22641

10 International Journal of Forestry Research

Table 11 Allometric equations for estimating branch biomass using DBH

Function Equation MRE R2 SEEExponential BR = 4644e0069Dbh 1172 093 075Logarithmic BR = 1056ln(DBH) +1534 002 084 072Polynomial BR = 0077DBH2 + 3373DBH +0213 - 453 099 058Linear BR = 0941DBH+ 1324 003 096 073Power BR = 1901DBH0793 1159 099 073s

Table 12 Allometric equations for estimating foliage using DBH

Function Equation MRE R2 SEEExponential F = 4795e0045DBH 274 097 024Logarithmic F = 362ln(DBH) + 4020 002 084 022Polynomial F = -0031DBH2 + 1270DBH + 3235 -183 099 058Linear F = 0295DBH + 8452 0003 097 023Power F= 2213DBH0596 -237 098 023

Table 13 Allometric equations for estimating TTB using HT

Function Equation MRE R2 SEEExponential TTB = 3090e0266HT -3750 054 1010Logarithmic TTB = 3157ln(HT) ndash 5973 006 093 300Polynomial TTB = -00409HT2 + 1863HT + 1327 021 099 252Linear TTB = 2969HT- 1980 002 074 255Power TTB= 0401HT1642 -544 097 053

Table 14 Allometric equations for estimating AGB using HT

Function Equation MRE R2 SEEExponential AGB = 2454e0263HT -2437 054 744Logarithmic AGB = 2401ln(H) ndash 4526 0084 093 248Polynomial AGB= -0312HT2 + 1411HT- 9872 024 099 210Linear AGB= 2255HT-14850 002 070 212Power AGB= 0027HT3174 793 082 286

Table 15 Allometric equations for estimating BGB using HT

Function Equation MRE R2 SEEExponential BGB = 0631e0269HT -622 053 226Logarithmic BGB = 707ln(HT) - 1333 -004 093 079Polynomial BGB = -0067HT2 + 4781HTndash3258 015 1 071Linear BGB = 6009HTndash4345 010 064 2352Power BGB= 0006HT3241 584 080 3134

Table 16 Allometric equations for estimating TTB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential TTB= 2348e0006P -761 073 667Logarithmic TTB= 1077ln(P) - 3397 0002 072 285Polynomial TTB = -0000P2 + 111Pndash205 -402 I 252Linear TTB = 0829Pndash0929 006 090 158Power TTB= 0395P1125 215 098 268

International Journal of Forestry Research 11

Table 17 Allometric equations for estimating AGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential AGB = 1826e00006P -746 073 524Logarithmic AGB = 8222ln(P) ndash 2581 -688 072 231Polynomial AGB = -0000P2 + 0829Pndash1609 -29 1 185Linear AGB = 0630P + 0965 019 086 146Power AGB= 0310P1119 3837 099 152

Table 18 Allometric equations for estimating BGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential BGB = 495e00006P 134 073 -145Logarithmic BGB = 2424ln(P) ndash 7622 001 072 075Polynomial BGB = -0000P2 + 0255Pndash5495 -101 1 069Linear BGB = 0184P + 0575 007 078 075Power BGB= 0084P1125 306 099 075

Table 19 Generated TTB from developed equation using DBH

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM128 1295594 139 1474242 186 2336786 303 518241424 418944 1 6674 17 20251 298 50404221 6674 92 7725136 91 7593304 1 66741 6674 1 6674 188 2377058 44 221838444 2218384 1 6674 146 1592514 265 414892154 173205 135 140826 185 231676 1 667416 183976 1 6674 25 502 1 667410 8806 16 183976 16 183976 1 667410 8806 3 9282 194 2499618 16 18397613 132742 154 173205 108 9933456 18 221772128 1295594 215 294922 153 1714354 135 140826209 2817486 17 142064 128 1295594 1 667422 255016 122 1201862 162 1876246 148 162696219 241762 8 61912 209 2817486 175 212052 094 876 7150521 19 241762 16 18397689 7331824 13 132742 22 255016 15 1661714 371576 1 6674 78 5945736 185 23167612 520944 1 6674 52 3019696 14 149092165 193152 1 6674 45 2316 165 193152126 1264058 15 2958 45 2316 126 1264058153 1714354 1 6674 24 418944 153 171435413 132742 2 094 42 2025336 1 6674118 114083 97 8395216 51 2916984 13 13274214 371576 96 8259744 25 502 118 11408333 1192656 122 1201862 45 2316 145 1575415 2958 87 7073256 54 3227304 171 20440342 094 83 6564856 26 585784 1 66741 6674 109 1007766 1 6674 1 6674171 2044034 68 4762096 1 6674 18 221772171 2044034 69 4877184 9 74622 1 6674

12 International Journal of Forestry Research

Table 19 Continued

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM9 74622 29 841504 105 95052 124 1232814114 1080962 1 6674 46 2414344 114 1080962108 9933456 51 2916984 1 6674 108 993345611 102226 11 102226 1 6674 93 7857696105 95052 1 6674 1 6674 118 11408312 11712 12 11712 1 6674 156 17676627 4993 104 9363904 1 6674 7 4993122 1201862 52 3019696 7 4993 175 21205111 1036826 111 1036826 53 3123136 144 155835813 132742 61 3976864 13 446624 118 11408310 8806 1 6674 18 064104 10 8806128 1295594 128 1295594 1 6674 13 13274220 26248 68 4762096 1 6674 8 619121 6674 1 6674 1 6674 138 1457638104 9363904 1 6674 1 6674 114 108096214 149092 1 6674 98 8531416 154 17320516 183976 104 9363904 1 6674 84 6690864195 25203 62 4086856 1 6674 78 594573681 6315024 95 8125 28 755536 225 3174656 3437824 85 68176 49 2713744 1 667452 3019696 65 44212 42 2025336 156 176766210 8806 81 6315024 121 1186494 1 667413 132742 1 6674 87 7073256 1 6674169 2006238 1 6674 56 3437824 29 84150421 283926 82 6439576 1 6674 136 142464621 283926 57 3544176 15 16617 164 191302213 132742 1 6674 202 266711 1 667439 1741224 6 38676 297 5012242 1 6674173 2082122 1 6674 195 25203 17 2025116 183976 1 6674 23 329002 16 18397616 183976 1 6674 23 336616 187 235688621 283926 64 4309024 183 2276926 104 9363904187 2356886 48 2613216 12 11712 122 120186239 1741224 1 6674 54 3227304 13 132742132 1359538 1 6674 132 1359538 18 22177218 221772 1 6674 2 094 1 667458 3651256 15 2958 1 6674 1 6674

36 Biomass Stocks amongAgroecological Zones Based on theallometric equations the average TTB for G robusta treesgenerated in each of the AEZ studied is as shown in Table 9The TTB stock for each AEZ was 13 926 tonhaminus1 13109tonhaminus1 10869 tonhaminus1 and 11827 tonhaminus1 in UM1 UM2UM3 and UM4 respectively Variability of tree biomassbetween the four agroecological zones showed no significantdifference (p-value gt 005) implying that though there couldbe a slight difference in the allometry of the tree speciesamong AEZ the total biomass does not vary This alsoexplains that the management of G robusta trees in the

agricultural landscapes of the four AEZ does not differ andthe farmers can form a marketing unit despite their differentAEZ and their production quotas can be the same

The average biomass stock of 1243 tonha in the studycompares well with the findings of Albrecht [20] 2-22tonha Henry [1] 9ndash11tonha and Kuya [5] 16 tonhaall of which are for agricultural landscapes This findinggives a better glimpse of the tree component in agricul-tural landscapes and is a good guide for the develop-ment of carbon stock factors in agricultural landscapes[21] With this moderate stock the farmers are able to

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

6 International Journal of Forestry Research

Table 6 Allometric equations for estimating various biomass using DBH

Function Equations MRE R2 SEEExponential TTB = 1091e0150DBH -2910 084 457Power TTB = 1811DBH1658 505 098 134Polynomial TTB = 0322DBBH2+793DBH-1926 015 093 133Linear TTB= 1800DBH - 7322 007 091 152Multiple TTB = 11356DBH ndash 8924HT + 0536(DBHlowastHT) + 1827 -016 093 140Exponential AGB=8474e0150DBH -2260 083 356Power AGB=1384DBH1665 32 098 099Linear AGB=1399DBH - 5696 002 092 112Polynomial AGB=0248DBH2 + 6243DBH ndash 1545 0002 094 099Multiple AGB=8641DBH ndash 69HT + 0424(DBHlowastHT) + 1453 006 090 198Exponential BGB = 2311e0151DBH -513 082 104Polynomial BGB = 0074DBH2+1688DBH ndash 3791 010 082 050Linear BGB = 4013DBH - 1624 -001 081 053Multiple BGB =2713DBH ndash 2028HT + 0111(DBHlowastHT) +379 010 082 051Power BGB = 0401DBH1642 342 093 051

the fitted regression line [14]These illustrations are shown inFigures 3 4 and 5

A comparison of functions for estimating TTB fromDBHillustrates that the exponential function overestimates DBHfor a tree of 35cm DBH Though the other three functionshave a near similar estimate the R2 values favor the powerfunction (R2 = 097) and the polynomial function (R2= 093)Though the linear function gives relatives good R2 valueforesters have disqualified linear relationships because theydo not illustrate the ideal relationship between predictorvariables and biomass or volume over a wide diameter sizedistribution [8 16]

Estimation of total tree biomass from height variedgreatly among functions making it difficult to select the idealfunction The R2 values were also lower compared to thoseof using DBH as a predictor variable The same trend wasnoted in estimating ABG from tree height Noting that heightmeasurement in forests is difficult and the fact that farmerssell trees while standing the use of tree height may increasetree biomass or volume estimation costs while not increasingaccuracy of estimates As such trials of height as a biomass-predictor variable were discarded in favor of DBH which iseasy to measure and can be measured with high levels ofaccuracy [6 8]

DBH gives a good estimate of AGB based on R2 valueswith 098 for the power function and 094 for the polynomialfunction Kuya [5] identified power functions as most idealfor estimating AGB in western Kenya while Henry et al[1] preferred polynomial functions It has been found thateither of these functions is ideal based on the diametersize distribution [8] Kuya [5] preferred power functionsbecause of the large DBH size distribution which disqualifiespolynomial functions which often have two turning points[14] and may not define the biomass-predictor relationshipover a wide range of diameter sizes In this case where Grobusta does not grow to large sizes in the study area either a

polynomial or a power function becomes ideal based on thiscriteria of choice

34 Choice of Equation Based on Standard Error of Estimateand Mean Residual Error Apart from the coefficient ofdetermination the standard error of estimate (SEE) and themean residual error (MRE) have been used in choice ofappropriate regression equations [14] The SEE is a measureof the accuracy of predictionsmadewith a regression line andthe lower the value the better the accuracy of an allometricequation [8] Zar [14] also explains the mean residual erroras another measure of the accuracy of a regression equationSince residuals are differences between the data points andthe regression line the mean residual error refers to the errorthat is not explained by the regression line

The choice of equation based on the three statistics isillustrated for the various biomass components in Table 6

Though linear functions had the least MRE for TTB andBGB their previously described limitations [8 14] disqual-ifies them The polynomial functions have very small MREvalues in all estimated biomass components of TTB (015kg)AGB (0002Kg) and BGB (01Kg) illustrating their appropri-ateness based on this second selection criteria Exponentialfunctions have large mean bias in all functions and thisfurther illustrates their inappropriateness in this selectionA bias of less than 5 of the total tree biomass is withinacceptable range [16 17] and would provide the farmers withthe real value of the tree In this case the polynomial functionis very accurate with very minimal bias within the range ofdiameter sizes tested

Based on the SEE the polynomial function gave thelowest values at 133 for TTB 099 for ABG and 05 forBGBThis compared well with the power function which had134 for TTB 099 for AGB and 051 for BGB In this thirdselection criteria the polynomial function again takes bestpreference

International Journal of Forestry Research 7

y = 18005x - 73223Rsup2 = 091

Linear Function

y = 10915e01504x

Rsup2 = 08361

Exponential function

y = 03223x 2 + 79347x - 19265 Rsup2 = 093

polynomial function

y = 1811x1658

Rsup2 = 09769

Power function

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0200400600800

10001200

Biom

ass (

Kg)

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

Figure 3 Comparison of functions for estimating total tree biomass from DBH

y = 30725e02672x

Rsup2 = 07813

Exponential Function

y = 29775x - 19625 Rsup2 = 07373

0 10 20 30

Tree Height (m)

Linear Function

y = 00332x32166

Rsup2 = 08693

Power Functiony = 03387x2 + 20641x - 14234

Rsup2 = 0741

0 10 20 30

Tree Height (m)

Polynomial Function

0

500

1000

1500

2000

2500

Biom

ass (

Kg)

10 20 300Tree Height (m) minus200

minus1000

100200300400500600

Biom

ass (

Kg)

minus200

0

200

400

600

800

Biom

ass (

Kg)

0200400600800

10001200

Biom

ass (

Kg)

10 20 300Tree Height (m)

Figure 4 A comparison of functions for estimating total tree biomass from tree height

Based on the statistics Table 7 shows the list of preferredequations for estimating the different tree biomass compo-nents Though all the preferred equations are polynomialfunctions it should be noted that the power functions werethe next best alternative and their application has alreadybeen illustrated for agroforestry species of western Kenya [5]The limitation of two turning points observed in polynomialfunctions [14] may not apply in the study area where Grobusta grows because the trees do not grow beyond the40cm DBH size that was used in this study It is howeverrecommended that such equations should not be appliedwhere trees of bigger sizes grow

Table 7 A list of selected allometric equations for estimatingbiomass components

Biomass component EquationsTotal Tree TTB = 0322DBBH2+793DBH-1926Above ground AGB=0248DBH2 + 6243DBH ndash 1545Below ground BGB = 0074DBH2+1688DBH ndash 3791Branches BRA = 0030DBH2 + 1574DBH ndash 4984Foliage F = 004DBH2 + 1949DBH ndash 3134

8 International Journal of Forestry Research

y = 1384x16658

Rsup2 = 09798

Power function

y = 13992x - 56966 Rsup2 = 09177

0 10 20 30 40

DBH (cm)

Linear function

y = 84746e01506x

Rsup2 = 0833

Exponential function

y = 0248x2 + 62437x - 15451 Rsup2 = 09374

0 10 20 30 40

DBH (cm)

Polynomial function

0

200

400

600

800

Biom

ass (

Kg)

10 20 30 400DBH (cm) minus100

0

100

200

300

400

500

Biom

ass (

Kg)

minus100

0

100

200

300

400

500

Biom

ass (

Kg)

0

100

200

300

400

500

Biom

ass (

Kg)

10 20 30 400DBH (cm)

Figure 5 A comparison of functions for estimating above ground tree biomass from DBH

Table 8 A validation of the equation with similar equations using the F values of the paired t-test

Author F calculated F critical Comments Discussion

Kuya [5] 15375557 18283There is nosignificantdifference

The Kuya equation was developed insimilar Agroforestry conditions but in a

different AEZs of Kenya

Henry [1] 0817302 18283There is nosignificantdifference

The equation was developed forAgroforestry trees of Western Kenya in a

different AEZ

Benedicto [19] 2070408 18408There is asignificantdifference

The equation was developed in Mexico Atotally different biome and may not be

applicable in the study area

Rurangwa [18] 1118687 18408There is nosignificantdifference

Rurangwa developed this equation inAgroforestry trees of Ruanda which is

within East Africa

Table 9 Average biomass values per hectare in AEZs

Component Average biomass (Kg) per hectareUM 1 UM 2 UM 3 UM 4

Foliage 922128 874343 724966 788837Branchesfoliage 1964818 1849623 1533623 1668739Rootsbelowground biomass 3109676 2927150 2427314 2640889Stemtrunk 7929378 7457484 6183147 6728175Total for tree 1392600 1310860 1086905 1182664

35 Validation of Developed Allometric Equations Validationof the equations based on the bias of the equation inestimating specific diameter sizes is illustrated in residualplots used to assist in validation which are shown in Figure 6

A second validation to compare biomass estimates fromthe preferred equation and that of similar studies showsthat the developed equation compares well with otherequations developed in agroforestry conditions of Kenya

[1 5] and Rwanda [18] but is not applicable in biomes farfrom the study area [19] This finding illustrates that theprocess of destructive sampling to develop new allomet-ric equations within a small geographical range may notenhance accuracy of estimates and an equation applicablein a similar land and tree management activity may as wellbe applicable in another one The results are illustrated inTable 8

International Journal of Forestry Research 9

0 10 20 30 40

DBH (cm)

Difference (Kg) Power function

0 10 20 30 40

DBH (cm)

Difference (Kg) Polynomial function

minus100

minus50

0

50

100Bi

omas

s res

idua

ls (k

g)

minus150

minus100

minus50

0

50

Biom

ass r

esid

uals

(kg)

Figure 6 Residual scatter plots of total tree biomass using polynomial and power function for TTB

Table 10 Total tree biomass and tree component biomass data of the 33 trees destructively sampled per every Agroecological Zone (AEZ)

AEZ Tree No DBH (cm) Height (m) Dry weights of biomass in kgStem Branches foliage AGB BGB TTB

UM4

1 52 655 1016 1625 522 1701 382 20832 15 36 155 0644 102 331 0801 4013 12 143 9369 1062 121 11641 3743 153844 132 127 7022 1108 1749 9879 2346 122255 225 167 16666 503 2292 23988 6314 303026 298 145 24752 8042 2127 34921 11955 468767V 18 60 165 033 0662 264 1461 4108V 137 145 11222 2661 1464 15347 3242 185899V 20 161 13487 315 1375 18012 5779 23791

UM3

10 120 1275 5901 688 1314 7903 324 1114311 154 137 1094 2475 2065 1548 5363 2084312 70 865 2038 50 75 3288 983 427113 56 865 1268 28 413 1961 594 255514 276 190 27053 9298 1797 38148 13037 5118515 277 192 30655 8325 160 4058 12708 5328816V 169 122 11803 4365 2239 18407 8603 270117V 98 91 3269 100 102 5289 1501 679418V 258 166 27516 6358 3326 3720 7495 44695

UM2

19 17 71 195 06 145 40 179 57920 87 98 2498 643 875 4016 786 480221 153 143 5883 385 1551 11284 2146 1343022 148 150 6963 3271 1046 1128 3399 1467923V 122 124 4063 1393 135 6806 1775 858124V 128 154 6294 1915 70 8909 2726 1163525 220 170 16471 3003 1109 20583 6836 2741926 298 212 2598 332 1089 30389 7934 3832327V 278 248 32763 439 871 38024 11475 49499

UM1

28 20 60 321 094 119 534 101 63529 89 99 2887 1025 1001 4913 590 550330V 45 91 1196 25 386 1832 360 219231 128 130 11466 3150 3122 17738 6522 242632 249 190 26284 3775 1857 31916 5650 3756633 204 115 12871 469 162 19181 3460 22641

10 International Journal of Forestry Research

Table 11 Allometric equations for estimating branch biomass using DBH

Function Equation MRE R2 SEEExponential BR = 4644e0069Dbh 1172 093 075Logarithmic BR = 1056ln(DBH) +1534 002 084 072Polynomial BR = 0077DBH2 + 3373DBH +0213 - 453 099 058Linear BR = 0941DBH+ 1324 003 096 073Power BR = 1901DBH0793 1159 099 073s

Table 12 Allometric equations for estimating foliage using DBH

Function Equation MRE R2 SEEExponential F = 4795e0045DBH 274 097 024Logarithmic F = 362ln(DBH) + 4020 002 084 022Polynomial F = -0031DBH2 + 1270DBH + 3235 -183 099 058Linear F = 0295DBH + 8452 0003 097 023Power F= 2213DBH0596 -237 098 023

Table 13 Allometric equations for estimating TTB using HT

Function Equation MRE R2 SEEExponential TTB = 3090e0266HT -3750 054 1010Logarithmic TTB = 3157ln(HT) ndash 5973 006 093 300Polynomial TTB = -00409HT2 + 1863HT + 1327 021 099 252Linear TTB = 2969HT- 1980 002 074 255Power TTB= 0401HT1642 -544 097 053

Table 14 Allometric equations for estimating AGB using HT

Function Equation MRE R2 SEEExponential AGB = 2454e0263HT -2437 054 744Logarithmic AGB = 2401ln(H) ndash 4526 0084 093 248Polynomial AGB= -0312HT2 + 1411HT- 9872 024 099 210Linear AGB= 2255HT-14850 002 070 212Power AGB= 0027HT3174 793 082 286

Table 15 Allometric equations for estimating BGB using HT

Function Equation MRE R2 SEEExponential BGB = 0631e0269HT -622 053 226Logarithmic BGB = 707ln(HT) - 1333 -004 093 079Polynomial BGB = -0067HT2 + 4781HTndash3258 015 1 071Linear BGB = 6009HTndash4345 010 064 2352Power BGB= 0006HT3241 584 080 3134

Table 16 Allometric equations for estimating TTB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential TTB= 2348e0006P -761 073 667Logarithmic TTB= 1077ln(P) - 3397 0002 072 285Polynomial TTB = -0000P2 + 111Pndash205 -402 I 252Linear TTB = 0829Pndash0929 006 090 158Power TTB= 0395P1125 215 098 268

International Journal of Forestry Research 11

Table 17 Allometric equations for estimating AGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential AGB = 1826e00006P -746 073 524Logarithmic AGB = 8222ln(P) ndash 2581 -688 072 231Polynomial AGB = -0000P2 + 0829Pndash1609 -29 1 185Linear AGB = 0630P + 0965 019 086 146Power AGB= 0310P1119 3837 099 152

Table 18 Allometric equations for estimating BGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential BGB = 495e00006P 134 073 -145Logarithmic BGB = 2424ln(P) ndash 7622 001 072 075Polynomial BGB = -0000P2 + 0255Pndash5495 -101 1 069Linear BGB = 0184P + 0575 007 078 075Power BGB= 0084P1125 306 099 075

Table 19 Generated TTB from developed equation using DBH

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM128 1295594 139 1474242 186 2336786 303 518241424 418944 1 6674 17 20251 298 50404221 6674 92 7725136 91 7593304 1 66741 6674 1 6674 188 2377058 44 221838444 2218384 1 6674 146 1592514 265 414892154 173205 135 140826 185 231676 1 667416 183976 1 6674 25 502 1 667410 8806 16 183976 16 183976 1 667410 8806 3 9282 194 2499618 16 18397613 132742 154 173205 108 9933456 18 221772128 1295594 215 294922 153 1714354 135 140826209 2817486 17 142064 128 1295594 1 667422 255016 122 1201862 162 1876246 148 162696219 241762 8 61912 209 2817486 175 212052 094 876 7150521 19 241762 16 18397689 7331824 13 132742 22 255016 15 1661714 371576 1 6674 78 5945736 185 23167612 520944 1 6674 52 3019696 14 149092165 193152 1 6674 45 2316 165 193152126 1264058 15 2958 45 2316 126 1264058153 1714354 1 6674 24 418944 153 171435413 132742 2 094 42 2025336 1 6674118 114083 97 8395216 51 2916984 13 13274214 371576 96 8259744 25 502 118 11408333 1192656 122 1201862 45 2316 145 1575415 2958 87 7073256 54 3227304 171 20440342 094 83 6564856 26 585784 1 66741 6674 109 1007766 1 6674 1 6674171 2044034 68 4762096 1 6674 18 221772171 2044034 69 4877184 9 74622 1 6674

12 International Journal of Forestry Research

Table 19 Continued

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM9 74622 29 841504 105 95052 124 1232814114 1080962 1 6674 46 2414344 114 1080962108 9933456 51 2916984 1 6674 108 993345611 102226 11 102226 1 6674 93 7857696105 95052 1 6674 1 6674 118 11408312 11712 12 11712 1 6674 156 17676627 4993 104 9363904 1 6674 7 4993122 1201862 52 3019696 7 4993 175 21205111 1036826 111 1036826 53 3123136 144 155835813 132742 61 3976864 13 446624 118 11408310 8806 1 6674 18 064104 10 8806128 1295594 128 1295594 1 6674 13 13274220 26248 68 4762096 1 6674 8 619121 6674 1 6674 1 6674 138 1457638104 9363904 1 6674 1 6674 114 108096214 149092 1 6674 98 8531416 154 17320516 183976 104 9363904 1 6674 84 6690864195 25203 62 4086856 1 6674 78 594573681 6315024 95 8125 28 755536 225 3174656 3437824 85 68176 49 2713744 1 667452 3019696 65 44212 42 2025336 156 176766210 8806 81 6315024 121 1186494 1 667413 132742 1 6674 87 7073256 1 6674169 2006238 1 6674 56 3437824 29 84150421 283926 82 6439576 1 6674 136 142464621 283926 57 3544176 15 16617 164 191302213 132742 1 6674 202 266711 1 667439 1741224 6 38676 297 5012242 1 6674173 2082122 1 6674 195 25203 17 2025116 183976 1 6674 23 329002 16 18397616 183976 1 6674 23 336616 187 235688621 283926 64 4309024 183 2276926 104 9363904187 2356886 48 2613216 12 11712 122 120186239 1741224 1 6674 54 3227304 13 132742132 1359538 1 6674 132 1359538 18 22177218 221772 1 6674 2 094 1 667458 3651256 15 2958 1 6674 1 6674

36 Biomass Stocks amongAgroecological Zones Based on theallometric equations the average TTB for G robusta treesgenerated in each of the AEZ studied is as shown in Table 9The TTB stock for each AEZ was 13 926 tonhaminus1 13109tonhaminus1 10869 tonhaminus1 and 11827 tonhaminus1 in UM1 UM2UM3 and UM4 respectively Variability of tree biomassbetween the four agroecological zones showed no significantdifference (p-value gt 005) implying that though there couldbe a slight difference in the allometry of the tree speciesamong AEZ the total biomass does not vary This alsoexplains that the management of G robusta trees in the

agricultural landscapes of the four AEZ does not differ andthe farmers can form a marketing unit despite their differentAEZ and their production quotas can be the same

The average biomass stock of 1243 tonha in the studycompares well with the findings of Albrecht [20] 2-22tonha Henry [1] 9ndash11tonha and Kuya [5] 16 tonhaall of which are for agricultural landscapes This findinggives a better glimpse of the tree component in agricul-tural landscapes and is a good guide for the develop-ment of carbon stock factors in agricultural landscapes[21] With this moderate stock the farmers are able to

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

International Journal of Forestry Research 7

y = 18005x - 73223Rsup2 = 091

Linear Function

y = 10915e01504x

Rsup2 = 08361

Exponential function

y = 03223x 2 + 79347x - 19265 Rsup2 = 093

polynomial function

y = 1811x1658

Rsup2 = 09769

Power function

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0200400600800

10001200

Biom

ass (

Kg)

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

0100200300400500600

Biom

ass (

Kg)

10 20 30 400DBH

Figure 3 Comparison of functions for estimating total tree biomass from DBH

y = 30725e02672x

Rsup2 = 07813

Exponential Function

y = 29775x - 19625 Rsup2 = 07373

0 10 20 30

Tree Height (m)

Linear Function

y = 00332x32166

Rsup2 = 08693

Power Functiony = 03387x2 + 20641x - 14234

Rsup2 = 0741

0 10 20 30

Tree Height (m)

Polynomial Function

0

500

1000

1500

2000

2500

Biom

ass (

Kg)

10 20 300Tree Height (m) minus200

minus1000

100200300400500600

Biom

ass (

Kg)

minus200

0

200

400

600

800

Biom

ass (

Kg)

0200400600800

10001200

Biom

ass (

Kg)

10 20 300Tree Height (m)

Figure 4 A comparison of functions for estimating total tree biomass from tree height

Based on the statistics Table 7 shows the list of preferredequations for estimating the different tree biomass compo-nents Though all the preferred equations are polynomialfunctions it should be noted that the power functions werethe next best alternative and their application has alreadybeen illustrated for agroforestry species of western Kenya [5]The limitation of two turning points observed in polynomialfunctions [14] may not apply in the study area where Grobusta grows because the trees do not grow beyond the40cm DBH size that was used in this study It is howeverrecommended that such equations should not be appliedwhere trees of bigger sizes grow

Table 7 A list of selected allometric equations for estimatingbiomass components

Biomass component EquationsTotal Tree TTB = 0322DBBH2+793DBH-1926Above ground AGB=0248DBH2 + 6243DBH ndash 1545Below ground BGB = 0074DBH2+1688DBH ndash 3791Branches BRA = 0030DBH2 + 1574DBH ndash 4984Foliage F = 004DBH2 + 1949DBH ndash 3134

8 International Journal of Forestry Research

y = 1384x16658

Rsup2 = 09798

Power function

y = 13992x - 56966 Rsup2 = 09177

0 10 20 30 40

DBH (cm)

Linear function

y = 84746e01506x

Rsup2 = 0833

Exponential function

y = 0248x2 + 62437x - 15451 Rsup2 = 09374

0 10 20 30 40

DBH (cm)

Polynomial function

0

200

400

600

800

Biom

ass (

Kg)

10 20 30 400DBH (cm) minus100

0

100

200

300

400

500

Biom

ass (

Kg)

minus100

0

100

200

300

400

500

Biom

ass (

Kg)

0

100

200

300

400

500

Biom

ass (

Kg)

10 20 30 400DBH (cm)

Figure 5 A comparison of functions for estimating above ground tree biomass from DBH

Table 8 A validation of the equation with similar equations using the F values of the paired t-test

Author F calculated F critical Comments Discussion

Kuya [5] 15375557 18283There is nosignificantdifference

The Kuya equation was developed insimilar Agroforestry conditions but in a

different AEZs of Kenya

Henry [1] 0817302 18283There is nosignificantdifference

The equation was developed forAgroforestry trees of Western Kenya in a

different AEZ

Benedicto [19] 2070408 18408There is asignificantdifference

The equation was developed in Mexico Atotally different biome and may not be

applicable in the study area

Rurangwa [18] 1118687 18408There is nosignificantdifference

Rurangwa developed this equation inAgroforestry trees of Ruanda which is

within East Africa

Table 9 Average biomass values per hectare in AEZs

Component Average biomass (Kg) per hectareUM 1 UM 2 UM 3 UM 4

Foliage 922128 874343 724966 788837Branchesfoliage 1964818 1849623 1533623 1668739Rootsbelowground biomass 3109676 2927150 2427314 2640889Stemtrunk 7929378 7457484 6183147 6728175Total for tree 1392600 1310860 1086905 1182664

35 Validation of Developed Allometric Equations Validationof the equations based on the bias of the equation inestimating specific diameter sizes is illustrated in residualplots used to assist in validation which are shown in Figure 6

A second validation to compare biomass estimates fromthe preferred equation and that of similar studies showsthat the developed equation compares well with otherequations developed in agroforestry conditions of Kenya

[1 5] and Rwanda [18] but is not applicable in biomes farfrom the study area [19] This finding illustrates that theprocess of destructive sampling to develop new allomet-ric equations within a small geographical range may notenhance accuracy of estimates and an equation applicablein a similar land and tree management activity may as wellbe applicable in another one The results are illustrated inTable 8

International Journal of Forestry Research 9

0 10 20 30 40

DBH (cm)

Difference (Kg) Power function

0 10 20 30 40

DBH (cm)

Difference (Kg) Polynomial function

minus100

minus50

0

50

100Bi

omas

s res

idua

ls (k

g)

minus150

minus100

minus50

0

50

Biom

ass r

esid

uals

(kg)

Figure 6 Residual scatter plots of total tree biomass using polynomial and power function for TTB

Table 10 Total tree biomass and tree component biomass data of the 33 trees destructively sampled per every Agroecological Zone (AEZ)

AEZ Tree No DBH (cm) Height (m) Dry weights of biomass in kgStem Branches foliage AGB BGB TTB

UM4

1 52 655 1016 1625 522 1701 382 20832 15 36 155 0644 102 331 0801 4013 12 143 9369 1062 121 11641 3743 153844 132 127 7022 1108 1749 9879 2346 122255 225 167 16666 503 2292 23988 6314 303026 298 145 24752 8042 2127 34921 11955 468767V 18 60 165 033 0662 264 1461 4108V 137 145 11222 2661 1464 15347 3242 185899V 20 161 13487 315 1375 18012 5779 23791

UM3

10 120 1275 5901 688 1314 7903 324 1114311 154 137 1094 2475 2065 1548 5363 2084312 70 865 2038 50 75 3288 983 427113 56 865 1268 28 413 1961 594 255514 276 190 27053 9298 1797 38148 13037 5118515 277 192 30655 8325 160 4058 12708 5328816V 169 122 11803 4365 2239 18407 8603 270117V 98 91 3269 100 102 5289 1501 679418V 258 166 27516 6358 3326 3720 7495 44695

UM2

19 17 71 195 06 145 40 179 57920 87 98 2498 643 875 4016 786 480221 153 143 5883 385 1551 11284 2146 1343022 148 150 6963 3271 1046 1128 3399 1467923V 122 124 4063 1393 135 6806 1775 858124V 128 154 6294 1915 70 8909 2726 1163525 220 170 16471 3003 1109 20583 6836 2741926 298 212 2598 332 1089 30389 7934 3832327V 278 248 32763 439 871 38024 11475 49499

UM1

28 20 60 321 094 119 534 101 63529 89 99 2887 1025 1001 4913 590 550330V 45 91 1196 25 386 1832 360 219231 128 130 11466 3150 3122 17738 6522 242632 249 190 26284 3775 1857 31916 5650 3756633 204 115 12871 469 162 19181 3460 22641

10 International Journal of Forestry Research

Table 11 Allometric equations for estimating branch biomass using DBH

Function Equation MRE R2 SEEExponential BR = 4644e0069Dbh 1172 093 075Logarithmic BR = 1056ln(DBH) +1534 002 084 072Polynomial BR = 0077DBH2 + 3373DBH +0213 - 453 099 058Linear BR = 0941DBH+ 1324 003 096 073Power BR = 1901DBH0793 1159 099 073s

Table 12 Allometric equations for estimating foliage using DBH

Function Equation MRE R2 SEEExponential F = 4795e0045DBH 274 097 024Logarithmic F = 362ln(DBH) + 4020 002 084 022Polynomial F = -0031DBH2 + 1270DBH + 3235 -183 099 058Linear F = 0295DBH + 8452 0003 097 023Power F= 2213DBH0596 -237 098 023

Table 13 Allometric equations for estimating TTB using HT

Function Equation MRE R2 SEEExponential TTB = 3090e0266HT -3750 054 1010Logarithmic TTB = 3157ln(HT) ndash 5973 006 093 300Polynomial TTB = -00409HT2 + 1863HT + 1327 021 099 252Linear TTB = 2969HT- 1980 002 074 255Power TTB= 0401HT1642 -544 097 053

Table 14 Allometric equations for estimating AGB using HT

Function Equation MRE R2 SEEExponential AGB = 2454e0263HT -2437 054 744Logarithmic AGB = 2401ln(H) ndash 4526 0084 093 248Polynomial AGB= -0312HT2 + 1411HT- 9872 024 099 210Linear AGB= 2255HT-14850 002 070 212Power AGB= 0027HT3174 793 082 286

Table 15 Allometric equations for estimating BGB using HT

Function Equation MRE R2 SEEExponential BGB = 0631e0269HT -622 053 226Logarithmic BGB = 707ln(HT) - 1333 -004 093 079Polynomial BGB = -0067HT2 + 4781HTndash3258 015 1 071Linear BGB = 6009HTndash4345 010 064 2352Power BGB= 0006HT3241 584 080 3134

Table 16 Allometric equations for estimating TTB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential TTB= 2348e0006P -761 073 667Logarithmic TTB= 1077ln(P) - 3397 0002 072 285Polynomial TTB = -0000P2 + 111Pndash205 -402 I 252Linear TTB = 0829Pndash0929 006 090 158Power TTB= 0395P1125 215 098 268

International Journal of Forestry Research 11

Table 17 Allometric equations for estimating AGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential AGB = 1826e00006P -746 073 524Logarithmic AGB = 8222ln(P) ndash 2581 -688 072 231Polynomial AGB = -0000P2 + 0829Pndash1609 -29 1 185Linear AGB = 0630P + 0965 019 086 146Power AGB= 0310P1119 3837 099 152

Table 18 Allometric equations for estimating BGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential BGB = 495e00006P 134 073 -145Logarithmic BGB = 2424ln(P) ndash 7622 001 072 075Polynomial BGB = -0000P2 + 0255Pndash5495 -101 1 069Linear BGB = 0184P + 0575 007 078 075Power BGB= 0084P1125 306 099 075

Table 19 Generated TTB from developed equation using DBH

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM128 1295594 139 1474242 186 2336786 303 518241424 418944 1 6674 17 20251 298 50404221 6674 92 7725136 91 7593304 1 66741 6674 1 6674 188 2377058 44 221838444 2218384 1 6674 146 1592514 265 414892154 173205 135 140826 185 231676 1 667416 183976 1 6674 25 502 1 667410 8806 16 183976 16 183976 1 667410 8806 3 9282 194 2499618 16 18397613 132742 154 173205 108 9933456 18 221772128 1295594 215 294922 153 1714354 135 140826209 2817486 17 142064 128 1295594 1 667422 255016 122 1201862 162 1876246 148 162696219 241762 8 61912 209 2817486 175 212052 094 876 7150521 19 241762 16 18397689 7331824 13 132742 22 255016 15 1661714 371576 1 6674 78 5945736 185 23167612 520944 1 6674 52 3019696 14 149092165 193152 1 6674 45 2316 165 193152126 1264058 15 2958 45 2316 126 1264058153 1714354 1 6674 24 418944 153 171435413 132742 2 094 42 2025336 1 6674118 114083 97 8395216 51 2916984 13 13274214 371576 96 8259744 25 502 118 11408333 1192656 122 1201862 45 2316 145 1575415 2958 87 7073256 54 3227304 171 20440342 094 83 6564856 26 585784 1 66741 6674 109 1007766 1 6674 1 6674171 2044034 68 4762096 1 6674 18 221772171 2044034 69 4877184 9 74622 1 6674

12 International Journal of Forestry Research

Table 19 Continued

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM9 74622 29 841504 105 95052 124 1232814114 1080962 1 6674 46 2414344 114 1080962108 9933456 51 2916984 1 6674 108 993345611 102226 11 102226 1 6674 93 7857696105 95052 1 6674 1 6674 118 11408312 11712 12 11712 1 6674 156 17676627 4993 104 9363904 1 6674 7 4993122 1201862 52 3019696 7 4993 175 21205111 1036826 111 1036826 53 3123136 144 155835813 132742 61 3976864 13 446624 118 11408310 8806 1 6674 18 064104 10 8806128 1295594 128 1295594 1 6674 13 13274220 26248 68 4762096 1 6674 8 619121 6674 1 6674 1 6674 138 1457638104 9363904 1 6674 1 6674 114 108096214 149092 1 6674 98 8531416 154 17320516 183976 104 9363904 1 6674 84 6690864195 25203 62 4086856 1 6674 78 594573681 6315024 95 8125 28 755536 225 3174656 3437824 85 68176 49 2713744 1 667452 3019696 65 44212 42 2025336 156 176766210 8806 81 6315024 121 1186494 1 667413 132742 1 6674 87 7073256 1 6674169 2006238 1 6674 56 3437824 29 84150421 283926 82 6439576 1 6674 136 142464621 283926 57 3544176 15 16617 164 191302213 132742 1 6674 202 266711 1 667439 1741224 6 38676 297 5012242 1 6674173 2082122 1 6674 195 25203 17 2025116 183976 1 6674 23 329002 16 18397616 183976 1 6674 23 336616 187 235688621 283926 64 4309024 183 2276926 104 9363904187 2356886 48 2613216 12 11712 122 120186239 1741224 1 6674 54 3227304 13 132742132 1359538 1 6674 132 1359538 18 22177218 221772 1 6674 2 094 1 667458 3651256 15 2958 1 6674 1 6674

36 Biomass Stocks amongAgroecological Zones Based on theallometric equations the average TTB for G robusta treesgenerated in each of the AEZ studied is as shown in Table 9The TTB stock for each AEZ was 13 926 tonhaminus1 13109tonhaminus1 10869 tonhaminus1 and 11827 tonhaminus1 in UM1 UM2UM3 and UM4 respectively Variability of tree biomassbetween the four agroecological zones showed no significantdifference (p-value gt 005) implying that though there couldbe a slight difference in the allometry of the tree speciesamong AEZ the total biomass does not vary This alsoexplains that the management of G robusta trees in the

agricultural landscapes of the four AEZ does not differ andthe farmers can form a marketing unit despite their differentAEZ and their production quotas can be the same

The average biomass stock of 1243 tonha in the studycompares well with the findings of Albrecht [20] 2-22tonha Henry [1] 9ndash11tonha and Kuya [5] 16 tonhaall of which are for agricultural landscapes This findinggives a better glimpse of the tree component in agricul-tural landscapes and is a good guide for the develop-ment of carbon stock factors in agricultural landscapes[21] With this moderate stock the farmers are able to

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

8 International Journal of Forestry Research

y = 1384x16658

Rsup2 = 09798

Power function

y = 13992x - 56966 Rsup2 = 09177

0 10 20 30 40

DBH (cm)

Linear function

y = 84746e01506x

Rsup2 = 0833

Exponential function

y = 0248x2 + 62437x - 15451 Rsup2 = 09374

0 10 20 30 40

DBH (cm)

Polynomial function

0

200

400

600

800

Biom

ass (

Kg)

10 20 30 400DBH (cm) minus100

0

100

200

300

400

500

Biom

ass (

Kg)

minus100

0

100

200

300

400

500

Biom

ass (

Kg)

0

100

200

300

400

500

Biom

ass (

Kg)

10 20 30 400DBH (cm)

Figure 5 A comparison of functions for estimating above ground tree biomass from DBH

Table 8 A validation of the equation with similar equations using the F values of the paired t-test

Author F calculated F critical Comments Discussion

Kuya [5] 15375557 18283There is nosignificantdifference

The Kuya equation was developed insimilar Agroforestry conditions but in a

different AEZs of Kenya

Henry [1] 0817302 18283There is nosignificantdifference

The equation was developed forAgroforestry trees of Western Kenya in a

different AEZ

Benedicto [19] 2070408 18408There is asignificantdifference

The equation was developed in Mexico Atotally different biome and may not be

applicable in the study area

Rurangwa [18] 1118687 18408There is nosignificantdifference

Rurangwa developed this equation inAgroforestry trees of Ruanda which is

within East Africa

Table 9 Average biomass values per hectare in AEZs

Component Average biomass (Kg) per hectareUM 1 UM 2 UM 3 UM 4

Foliage 922128 874343 724966 788837Branchesfoliage 1964818 1849623 1533623 1668739Rootsbelowground biomass 3109676 2927150 2427314 2640889Stemtrunk 7929378 7457484 6183147 6728175Total for tree 1392600 1310860 1086905 1182664

35 Validation of Developed Allometric Equations Validationof the equations based on the bias of the equation inestimating specific diameter sizes is illustrated in residualplots used to assist in validation which are shown in Figure 6

A second validation to compare biomass estimates fromthe preferred equation and that of similar studies showsthat the developed equation compares well with otherequations developed in agroforestry conditions of Kenya

[1 5] and Rwanda [18] but is not applicable in biomes farfrom the study area [19] This finding illustrates that theprocess of destructive sampling to develop new allomet-ric equations within a small geographical range may notenhance accuracy of estimates and an equation applicablein a similar land and tree management activity may as wellbe applicable in another one The results are illustrated inTable 8

International Journal of Forestry Research 9

0 10 20 30 40

DBH (cm)

Difference (Kg) Power function

0 10 20 30 40

DBH (cm)

Difference (Kg) Polynomial function

minus100

minus50

0

50

100Bi

omas

s res

idua

ls (k

g)

minus150

minus100

minus50

0

50

Biom

ass r

esid

uals

(kg)

Figure 6 Residual scatter plots of total tree biomass using polynomial and power function for TTB

Table 10 Total tree biomass and tree component biomass data of the 33 trees destructively sampled per every Agroecological Zone (AEZ)

AEZ Tree No DBH (cm) Height (m) Dry weights of biomass in kgStem Branches foliage AGB BGB TTB

UM4

1 52 655 1016 1625 522 1701 382 20832 15 36 155 0644 102 331 0801 4013 12 143 9369 1062 121 11641 3743 153844 132 127 7022 1108 1749 9879 2346 122255 225 167 16666 503 2292 23988 6314 303026 298 145 24752 8042 2127 34921 11955 468767V 18 60 165 033 0662 264 1461 4108V 137 145 11222 2661 1464 15347 3242 185899V 20 161 13487 315 1375 18012 5779 23791

UM3

10 120 1275 5901 688 1314 7903 324 1114311 154 137 1094 2475 2065 1548 5363 2084312 70 865 2038 50 75 3288 983 427113 56 865 1268 28 413 1961 594 255514 276 190 27053 9298 1797 38148 13037 5118515 277 192 30655 8325 160 4058 12708 5328816V 169 122 11803 4365 2239 18407 8603 270117V 98 91 3269 100 102 5289 1501 679418V 258 166 27516 6358 3326 3720 7495 44695

UM2

19 17 71 195 06 145 40 179 57920 87 98 2498 643 875 4016 786 480221 153 143 5883 385 1551 11284 2146 1343022 148 150 6963 3271 1046 1128 3399 1467923V 122 124 4063 1393 135 6806 1775 858124V 128 154 6294 1915 70 8909 2726 1163525 220 170 16471 3003 1109 20583 6836 2741926 298 212 2598 332 1089 30389 7934 3832327V 278 248 32763 439 871 38024 11475 49499

UM1

28 20 60 321 094 119 534 101 63529 89 99 2887 1025 1001 4913 590 550330V 45 91 1196 25 386 1832 360 219231 128 130 11466 3150 3122 17738 6522 242632 249 190 26284 3775 1857 31916 5650 3756633 204 115 12871 469 162 19181 3460 22641

10 International Journal of Forestry Research

Table 11 Allometric equations for estimating branch biomass using DBH

Function Equation MRE R2 SEEExponential BR = 4644e0069Dbh 1172 093 075Logarithmic BR = 1056ln(DBH) +1534 002 084 072Polynomial BR = 0077DBH2 + 3373DBH +0213 - 453 099 058Linear BR = 0941DBH+ 1324 003 096 073Power BR = 1901DBH0793 1159 099 073s

Table 12 Allometric equations for estimating foliage using DBH

Function Equation MRE R2 SEEExponential F = 4795e0045DBH 274 097 024Logarithmic F = 362ln(DBH) + 4020 002 084 022Polynomial F = -0031DBH2 + 1270DBH + 3235 -183 099 058Linear F = 0295DBH + 8452 0003 097 023Power F= 2213DBH0596 -237 098 023

Table 13 Allometric equations for estimating TTB using HT

Function Equation MRE R2 SEEExponential TTB = 3090e0266HT -3750 054 1010Logarithmic TTB = 3157ln(HT) ndash 5973 006 093 300Polynomial TTB = -00409HT2 + 1863HT + 1327 021 099 252Linear TTB = 2969HT- 1980 002 074 255Power TTB= 0401HT1642 -544 097 053

Table 14 Allometric equations for estimating AGB using HT

Function Equation MRE R2 SEEExponential AGB = 2454e0263HT -2437 054 744Logarithmic AGB = 2401ln(H) ndash 4526 0084 093 248Polynomial AGB= -0312HT2 + 1411HT- 9872 024 099 210Linear AGB= 2255HT-14850 002 070 212Power AGB= 0027HT3174 793 082 286

Table 15 Allometric equations for estimating BGB using HT

Function Equation MRE R2 SEEExponential BGB = 0631e0269HT -622 053 226Logarithmic BGB = 707ln(HT) - 1333 -004 093 079Polynomial BGB = -0067HT2 + 4781HTndash3258 015 1 071Linear BGB = 6009HTndash4345 010 064 2352Power BGB= 0006HT3241 584 080 3134

Table 16 Allometric equations for estimating TTB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential TTB= 2348e0006P -761 073 667Logarithmic TTB= 1077ln(P) - 3397 0002 072 285Polynomial TTB = -0000P2 + 111Pndash205 -402 I 252Linear TTB = 0829Pndash0929 006 090 158Power TTB= 0395P1125 215 098 268

International Journal of Forestry Research 11

Table 17 Allometric equations for estimating AGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential AGB = 1826e00006P -746 073 524Logarithmic AGB = 8222ln(P) ndash 2581 -688 072 231Polynomial AGB = -0000P2 + 0829Pndash1609 -29 1 185Linear AGB = 0630P + 0965 019 086 146Power AGB= 0310P1119 3837 099 152

Table 18 Allometric equations for estimating BGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential BGB = 495e00006P 134 073 -145Logarithmic BGB = 2424ln(P) ndash 7622 001 072 075Polynomial BGB = -0000P2 + 0255Pndash5495 -101 1 069Linear BGB = 0184P + 0575 007 078 075Power BGB= 0084P1125 306 099 075

Table 19 Generated TTB from developed equation using DBH

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM128 1295594 139 1474242 186 2336786 303 518241424 418944 1 6674 17 20251 298 50404221 6674 92 7725136 91 7593304 1 66741 6674 1 6674 188 2377058 44 221838444 2218384 1 6674 146 1592514 265 414892154 173205 135 140826 185 231676 1 667416 183976 1 6674 25 502 1 667410 8806 16 183976 16 183976 1 667410 8806 3 9282 194 2499618 16 18397613 132742 154 173205 108 9933456 18 221772128 1295594 215 294922 153 1714354 135 140826209 2817486 17 142064 128 1295594 1 667422 255016 122 1201862 162 1876246 148 162696219 241762 8 61912 209 2817486 175 212052 094 876 7150521 19 241762 16 18397689 7331824 13 132742 22 255016 15 1661714 371576 1 6674 78 5945736 185 23167612 520944 1 6674 52 3019696 14 149092165 193152 1 6674 45 2316 165 193152126 1264058 15 2958 45 2316 126 1264058153 1714354 1 6674 24 418944 153 171435413 132742 2 094 42 2025336 1 6674118 114083 97 8395216 51 2916984 13 13274214 371576 96 8259744 25 502 118 11408333 1192656 122 1201862 45 2316 145 1575415 2958 87 7073256 54 3227304 171 20440342 094 83 6564856 26 585784 1 66741 6674 109 1007766 1 6674 1 6674171 2044034 68 4762096 1 6674 18 221772171 2044034 69 4877184 9 74622 1 6674

12 International Journal of Forestry Research

Table 19 Continued

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM9 74622 29 841504 105 95052 124 1232814114 1080962 1 6674 46 2414344 114 1080962108 9933456 51 2916984 1 6674 108 993345611 102226 11 102226 1 6674 93 7857696105 95052 1 6674 1 6674 118 11408312 11712 12 11712 1 6674 156 17676627 4993 104 9363904 1 6674 7 4993122 1201862 52 3019696 7 4993 175 21205111 1036826 111 1036826 53 3123136 144 155835813 132742 61 3976864 13 446624 118 11408310 8806 1 6674 18 064104 10 8806128 1295594 128 1295594 1 6674 13 13274220 26248 68 4762096 1 6674 8 619121 6674 1 6674 1 6674 138 1457638104 9363904 1 6674 1 6674 114 108096214 149092 1 6674 98 8531416 154 17320516 183976 104 9363904 1 6674 84 6690864195 25203 62 4086856 1 6674 78 594573681 6315024 95 8125 28 755536 225 3174656 3437824 85 68176 49 2713744 1 667452 3019696 65 44212 42 2025336 156 176766210 8806 81 6315024 121 1186494 1 667413 132742 1 6674 87 7073256 1 6674169 2006238 1 6674 56 3437824 29 84150421 283926 82 6439576 1 6674 136 142464621 283926 57 3544176 15 16617 164 191302213 132742 1 6674 202 266711 1 667439 1741224 6 38676 297 5012242 1 6674173 2082122 1 6674 195 25203 17 2025116 183976 1 6674 23 329002 16 18397616 183976 1 6674 23 336616 187 235688621 283926 64 4309024 183 2276926 104 9363904187 2356886 48 2613216 12 11712 122 120186239 1741224 1 6674 54 3227304 13 132742132 1359538 1 6674 132 1359538 18 22177218 221772 1 6674 2 094 1 667458 3651256 15 2958 1 6674 1 6674

36 Biomass Stocks amongAgroecological Zones Based on theallometric equations the average TTB for G robusta treesgenerated in each of the AEZ studied is as shown in Table 9The TTB stock for each AEZ was 13 926 tonhaminus1 13109tonhaminus1 10869 tonhaminus1 and 11827 tonhaminus1 in UM1 UM2UM3 and UM4 respectively Variability of tree biomassbetween the four agroecological zones showed no significantdifference (p-value gt 005) implying that though there couldbe a slight difference in the allometry of the tree speciesamong AEZ the total biomass does not vary This alsoexplains that the management of G robusta trees in the

agricultural landscapes of the four AEZ does not differ andthe farmers can form a marketing unit despite their differentAEZ and their production quotas can be the same

The average biomass stock of 1243 tonha in the studycompares well with the findings of Albrecht [20] 2-22tonha Henry [1] 9ndash11tonha and Kuya [5] 16 tonhaall of which are for agricultural landscapes This findinggives a better glimpse of the tree component in agricul-tural landscapes and is a good guide for the develop-ment of carbon stock factors in agricultural landscapes[21] With this moderate stock the farmers are able to

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

International Journal of Forestry Research 9

0 10 20 30 40

DBH (cm)

Difference (Kg) Power function

0 10 20 30 40

DBH (cm)

Difference (Kg) Polynomial function

minus100

minus50

0

50

100Bi

omas

s res

idua

ls (k

g)

minus150

minus100

minus50

0

50

Biom

ass r

esid

uals

(kg)

Figure 6 Residual scatter plots of total tree biomass using polynomial and power function for TTB

Table 10 Total tree biomass and tree component biomass data of the 33 trees destructively sampled per every Agroecological Zone (AEZ)

AEZ Tree No DBH (cm) Height (m) Dry weights of biomass in kgStem Branches foliage AGB BGB TTB

UM4

1 52 655 1016 1625 522 1701 382 20832 15 36 155 0644 102 331 0801 4013 12 143 9369 1062 121 11641 3743 153844 132 127 7022 1108 1749 9879 2346 122255 225 167 16666 503 2292 23988 6314 303026 298 145 24752 8042 2127 34921 11955 468767V 18 60 165 033 0662 264 1461 4108V 137 145 11222 2661 1464 15347 3242 185899V 20 161 13487 315 1375 18012 5779 23791

UM3

10 120 1275 5901 688 1314 7903 324 1114311 154 137 1094 2475 2065 1548 5363 2084312 70 865 2038 50 75 3288 983 427113 56 865 1268 28 413 1961 594 255514 276 190 27053 9298 1797 38148 13037 5118515 277 192 30655 8325 160 4058 12708 5328816V 169 122 11803 4365 2239 18407 8603 270117V 98 91 3269 100 102 5289 1501 679418V 258 166 27516 6358 3326 3720 7495 44695

UM2

19 17 71 195 06 145 40 179 57920 87 98 2498 643 875 4016 786 480221 153 143 5883 385 1551 11284 2146 1343022 148 150 6963 3271 1046 1128 3399 1467923V 122 124 4063 1393 135 6806 1775 858124V 128 154 6294 1915 70 8909 2726 1163525 220 170 16471 3003 1109 20583 6836 2741926 298 212 2598 332 1089 30389 7934 3832327V 278 248 32763 439 871 38024 11475 49499

UM1

28 20 60 321 094 119 534 101 63529 89 99 2887 1025 1001 4913 590 550330V 45 91 1196 25 386 1832 360 219231 128 130 11466 3150 3122 17738 6522 242632 249 190 26284 3775 1857 31916 5650 3756633 204 115 12871 469 162 19181 3460 22641

10 International Journal of Forestry Research

Table 11 Allometric equations for estimating branch biomass using DBH

Function Equation MRE R2 SEEExponential BR = 4644e0069Dbh 1172 093 075Logarithmic BR = 1056ln(DBH) +1534 002 084 072Polynomial BR = 0077DBH2 + 3373DBH +0213 - 453 099 058Linear BR = 0941DBH+ 1324 003 096 073Power BR = 1901DBH0793 1159 099 073s

Table 12 Allometric equations for estimating foliage using DBH

Function Equation MRE R2 SEEExponential F = 4795e0045DBH 274 097 024Logarithmic F = 362ln(DBH) + 4020 002 084 022Polynomial F = -0031DBH2 + 1270DBH + 3235 -183 099 058Linear F = 0295DBH + 8452 0003 097 023Power F= 2213DBH0596 -237 098 023

Table 13 Allometric equations for estimating TTB using HT

Function Equation MRE R2 SEEExponential TTB = 3090e0266HT -3750 054 1010Logarithmic TTB = 3157ln(HT) ndash 5973 006 093 300Polynomial TTB = -00409HT2 + 1863HT + 1327 021 099 252Linear TTB = 2969HT- 1980 002 074 255Power TTB= 0401HT1642 -544 097 053

Table 14 Allometric equations for estimating AGB using HT

Function Equation MRE R2 SEEExponential AGB = 2454e0263HT -2437 054 744Logarithmic AGB = 2401ln(H) ndash 4526 0084 093 248Polynomial AGB= -0312HT2 + 1411HT- 9872 024 099 210Linear AGB= 2255HT-14850 002 070 212Power AGB= 0027HT3174 793 082 286

Table 15 Allometric equations for estimating BGB using HT

Function Equation MRE R2 SEEExponential BGB = 0631e0269HT -622 053 226Logarithmic BGB = 707ln(HT) - 1333 -004 093 079Polynomial BGB = -0067HT2 + 4781HTndash3258 015 1 071Linear BGB = 6009HTndash4345 010 064 2352Power BGB= 0006HT3241 584 080 3134

Table 16 Allometric equations for estimating TTB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential TTB= 2348e0006P -761 073 667Logarithmic TTB= 1077ln(P) - 3397 0002 072 285Polynomial TTB = -0000P2 + 111Pndash205 -402 I 252Linear TTB = 0829Pndash0929 006 090 158Power TTB= 0395P1125 215 098 268

International Journal of Forestry Research 11

Table 17 Allometric equations for estimating AGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential AGB = 1826e00006P -746 073 524Logarithmic AGB = 8222ln(P) ndash 2581 -688 072 231Polynomial AGB = -0000P2 + 0829Pndash1609 -29 1 185Linear AGB = 0630P + 0965 019 086 146Power AGB= 0310P1119 3837 099 152

Table 18 Allometric equations for estimating BGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential BGB = 495e00006P 134 073 -145Logarithmic BGB = 2424ln(P) ndash 7622 001 072 075Polynomial BGB = -0000P2 + 0255Pndash5495 -101 1 069Linear BGB = 0184P + 0575 007 078 075Power BGB= 0084P1125 306 099 075

Table 19 Generated TTB from developed equation using DBH

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM128 1295594 139 1474242 186 2336786 303 518241424 418944 1 6674 17 20251 298 50404221 6674 92 7725136 91 7593304 1 66741 6674 1 6674 188 2377058 44 221838444 2218384 1 6674 146 1592514 265 414892154 173205 135 140826 185 231676 1 667416 183976 1 6674 25 502 1 667410 8806 16 183976 16 183976 1 667410 8806 3 9282 194 2499618 16 18397613 132742 154 173205 108 9933456 18 221772128 1295594 215 294922 153 1714354 135 140826209 2817486 17 142064 128 1295594 1 667422 255016 122 1201862 162 1876246 148 162696219 241762 8 61912 209 2817486 175 212052 094 876 7150521 19 241762 16 18397689 7331824 13 132742 22 255016 15 1661714 371576 1 6674 78 5945736 185 23167612 520944 1 6674 52 3019696 14 149092165 193152 1 6674 45 2316 165 193152126 1264058 15 2958 45 2316 126 1264058153 1714354 1 6674 24 418944 153 171435413 132742 2 094 42 2025336 1 6674118 114083 97 8395216 51 2916984 13 13274214 371576 96 8259744 25 502 118 11408333 1192656 122 1201862 45 2316 145 1575415 2958 87 7073256 54 3227304 171 20440342 094 83 6564856 26 585784 1 66741 6674 109 1007766 1 6674 1 6674171 2044034 68 4762096 1 6674 18 221772171 2044034 69 4877184 9 74622 1 6674

12 International Journal of Forestry Research

Table 19 Continued

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM9 74622 29 841504 105 95052 124 1232814114 1080962 1 6674 46 2414344 114 1080962108 9933456 51 2916984 1 6674 108 993345611 102226 11 102226 1 6674 93 7857696105 95052 1 6674 1 6674 118 11408312 11712 12 11712 1 6674 156 17676627 4993 104 9363904 1 6674 7 4993122 1201862 52 3019696 7 4993 175 21205111 1036826 111 1036826 53 3123136 144 155835813 132742 61 3976864 13 446624 118 11408310 8806 1 6674 18 064104 10 8806128 1295594 128 1295594 1 6674 13 13274220 26248 68 4762096 1 6674 8 619121 6674 1 6674 1 6674 138 1457638104 9363904 1 6674 1 6674 114 108096214 149092 1 6674 98 8531416 154 17320516 183976 104 9363904 1 6674 84 6690864195 25203 62 4086856 1 6674 78 594573681 6315024 95 8125 28 755536 225 3174656 3437824 85 68176 49 2713744 1 667452 3019696 65 44212 42 2025336 156 176766210 8806 81 6315024 121 1186494 1 667413 132742 1 6674 87 7073256 1 6674169 2006238 1 6674 56 3437824 29 84150421 283926 82 6439576 1 6674 136 142464621 283926 57 3544176 15 16617 164 191302213 132742 1 6674 202 266711 1 667439 1741224 6 38676 297 5012242 1 6674173 2082122 1 6674 195 25203 17 2025116 183976 1 6674 23 329002 16 18397616 183976 1 6674 23 336616 187 235688621 283926 64 4309024 183 2276926 104 9363904187 2356886 48 2613216 12 11712 122 120186239 1741224 1 6674 54 3227304 13 132742132 1359538 1 6674 132 1359538 18 22177218 221772 1 6674 2 094 1 667458 3651256 15 2958 1 6674 1 6674

36 Biomass Stocks amongAgroecological Zones Based on theallometric equations the average TTB for G robusta treesgenerated in each of the AEZ studied is as shown in Table 9The TTB stock for each AEZ was 13 926 tonhaminus1 13109tonhaminus1 10869 tonhaminus1 and 11827 tonhaminus1 in UM1 UM2UM3 and UM4 respectively Variability of tree biomassbetween the four agroecological zones showed no significantdifference (p-value gt 005) implying that though there couldbe a slight difference in the allometry of the tree speciesamong AEZ the total biomass does not vary This alsoexplains that the management of G robusta trees in the

agricultural landscapes of the four AEZ does not differ andthe farmers can form a marketing unit despite their differentAEZ and their production quotas can be the same

The average biomass stock of 1243 tonha in the studycompares well with the findings of Albrecht [20] 2-22tonha Henry [1] 9ndash11tonha and Kuya [5] 16 tonhaall of which are for agricultural landscapes This findinggives a better glimpse of the tree component in agricul-tural landscapes and is a good guide for the develop-ment of carbon stock factors in agricultural landscapes[21] With this moderate stock the farmers are able to

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

10 International Journal of Forestry Research

Table 11 Allometric equations for estimating branch biomass using DBH

Function Equation MRE R2 SEEExponential BR = 4644e0069Dbh 1172 093 075Logarithmic BR = 1056ln(DBH) +1534 002 084 072Polynomial BR = 0077DBH2 + 3373DBH +0213 - 453 099 058Linear BR = 0941DBH+ 1324 003 096 073Power BR = 1901DBH0793 1159 099 073s

Table 12 Allometric equations for estimating foliage using DBH

Function Equation MRE R2 SEEExponential F = 4795e0045DBH 274 097 024Logarithmic F = 362ln(DBH) + 4020 002 084 022Polynomial F = -0031DBH2 + 1270DBH + 3235 -183 099 058Linear F = 0295DBH + 8452 0003 097 023Power F= 2213DBH0596 -237 098 023

Table 13 Allometric equations for estimating TTB using HT

Function Equation MRE R2 SEEExponential TTB = 3090e0266HT -3750 054 1010Logarithmic TTB = 3157ln(HT) ndash 5973 006 093 300Polynomial TTB = -00409HT2 + 1863HT + 1327 021 099 252Linear TTB = 2969HT- 1980 002 074 255Power TTB= 0401HT1642 -544 097 053

Table 14 Allometric equations for estimating AGB using HT

Function Equation MRE R2 SEEExponential AGB = 2454e0263HT -2437 054 744Logarithmic AGB = 2401ln(H) ndash 4526 0084 093 248Polynomial AGB= -0312HT2 + 1411HT- 9872 024 099 210Linear AGB= 2255HT-14850 002 070 212Power AGB= 0027HT3174 793 082 286

Table 15 Allometric equations for estimating BGB using HT

Function Equation MRE R2 SEEExponential BGB = 0631e0269HT -622 053 226Logarithmic BGB = 707ln(HT) - 1333 -004 093 079Polynomial BGB = -0067HT2 + 4781HTndash3258 015 1 071Linear BGB = 6009HTndash4345 010 064 2352Power BGB= 0006HT3241 584 080 3134

Table 16 Allometric equations for estimating TTB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential TTB= 2348e0006P -761 073 667Logarithmic TTB= 1077ln(P) - 3397 0002 072 285Polynomial TTB = -0000P2 + 111Pndash205 -402 I 252Linear TTB = 0829Pndash0929 006 090 158Power TTB= 0395P1125 215 098 268

International Journal of Forestry Research 11

Table 17 Allometric equations for estimating AGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential AGB = 1826e00006P -746 073 524Logarithmic AGB = 8222ln(P) ndash 2581 -688 072 231Polynomial AGB = -0000P2 + 0829Pndash1609 -29 1 185Linear AGB = 0630P + 0965 019 086 146Power AGB= 0310P1119 3837 099 152

Table 18 Allometric equations for estimating BGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential BGB = 495e00006P 134 073 -145Logarithmic BGB = 2424ln(P) ndash 7622 001 072 075Polynomial BGB = -0000P2 + 0255Pndash5495 -101 1 069Linear BGB = 0184P + 0575 007 078 075Power BGB= 0084P1125 306 099 075

Table 19 Generated TTB from developed equation using DBH

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM128 1295594 139 1474242 186 2336786 303 518241424 418944 1 6674 17 20251 298 50404221 6674 92 7725136 91 7593304 1 66741 6674 1 6674 188 2377058 44 221838444 2218384 1 6674 146 1592514 265 414892154 173205 135 140826 185 231676 1 667416 183976 1 6674 25 502 1 667410 8806 16 183976 16 183976 1 667410 8806 3 9282 194 2499618 16 18397613 132742 154 173205 108 9933456 18 221772128 1295594 215 294922 153 1714354 135 140826209 2817486 17 142064 128 1295594 1 667422 255016 122 1201862 162 1876246 148 162696219 241762 8 61912 209 2817486 175 212052 094 876 7150521 19 241762 16 18397689 7331824 13 132742 22 255016 15 1661714 371576 1 6674 78 5945736 185 23167612 520944 1 6674 52 3019696 14 149092165 193152 1 6674 45 2316 165 193152126 1264058 15 2958 45 2316 126 1264058153 1714354 1 6674 24 418944 153 171435413 132742 2 094 42 2025336 1 6674118 114083 97 8395216 51 2916984 13 13274214 371576 96 8259744 25 502 118 11408333 1192656 122 1201862 45 2316 145 1575415 2958 87 7073256 54 3227304 171 20440342 094 83 6564856 26 585784 1 66741 6674 109 1007766 1 6674 1 6674171 2044034 68 4762096 1 6674 18 221772171 2044034 69 4877184 9 74622 1 6674

12 International Journal of Forestry Research

Table 19 Continued

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM9 74622 29 841504 105 95052 124 1232814114 1080962 1 6674 46 2414344 114 1080962108 9933456 51 2916984 1 6674 108 993345611 102226 11 102226 1 6674 93 7857696105 95052 1 6674 1 6674 118 11408312 11712 12 11712 1 6674 156 17676627 4993 104 9363904 1 6674 7 4993122 1201862 52 3019696 7 4993 175 21205111 1036826 111 1036826 53 3123136 144 155835813 132742 61 3976864 13 446624 118 11408310 8806 1 6674 18 064104 10 8806128 1295594 128 1295594 1 6674 13 13274220 26248 68 4762096 1 6674 8 619121 6674 1 6674 1 6674 138 1457638104 9363904 1 6674 1 6674 114 108096214 149092 1 6674 98 8531416 154 17320516 183976 104 9363904 1 6674 84 6690864195 25203 62 4086856 1 6674 78 594573681 6315024 95 8125 28 755536 225 3174656 3437824 85 68176 49 2713744 1 667452 3019696 65 44212 42 2025336 156 176766210 8806 81 6315024 121 1186494 1 667413 132742 1 6674 87 7073256 1 6674169 2006238 1 6674 56 3437824 29 84150421 283926 82 6439576 1 6674 136 142464621 283926 57 3544176 15 16617 164 191302213 132742 1 6674 202 266711 1 667439 1741224 6 38676 297 5012242 1 6674173 2082122 1 6674 195 25203 17 2025116 183976 1 6674 23 329002 16 18397616 183976 1 6674 23 336616 187 235688621 283926 64 4309024 183 2276926 104 9363904187 2356886 48 2613216 12 11712 122 120186239 1741224 1 6674 54 3227304 13 132742132 1359538 1 6674 132 1359538 18 22177218 221772 1 6674 2 094 1 667458 3651256 15 2958 1 6674 1 6674

36 Biomass Stocks amongAgroecological Zones Based on theallometric equations the average TTB for G robusta treesgenerated in each of the AEZ studied is as shown in Table 9The TTB stock for each AEZ was 13 926 tonhaminus1 13109tonhaminus1 10869 tonhaminus1 and 11827 tonhaminus1 in UM1 UM2UM3 and UM4 respectively Variability of tree biomassbetween the four agroecological zones showed no significantdifference (p-value gt 005) implying that though there couldbe a slight difference in the allometry of the tree speciesamong AEZ the total biomass does not vary This alsoexplains that the management of G robusta trees in the

agricultural landscapes of the four AEZ does not differ andthe farmers can form a marketing unit despite their differentAEZ and their production quotas can be the same

The average biomass stock of 1243 tonha in the studycompares well with the findings of Albrecht [20] 2-22tonha Henry [1] 9ndash11tonha and Kuya [5] 16 tonhaall of which are for agricultural landscapes This findinggives a better glimpse of the tree component in agricul-tural landscapes and is a good guide for the develop-ment of carbon stock factors in agricultural landscapes[21] With this moderate stock the farmers are able to

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

International Journal of Forestry Research 11

Table 17 Allometric equations for estimating AGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential AGB = 1826e00006P -746 073 524Logarithmic AGB = 8222ln(P) ndash 2581 -688 072 231Polynomial AGB = -0000P2 + 0829Pndash1609 -29 1 185Linear AGB = 0630P + 0965 019 086 146Power AGB= 0310P1119 3837 099 152

Table 18 Allometric equations for estimating BGB using combination of DBH and HT (DBHlowastHT = P)

Function Equation MRE R2 SEEExponential BGB = 495e00006P 134 073 -145Logarithmic BGB = 2424ln(P) ndash 7622 001 072 075Polynomial BGB = -0000P2 + 0255Pndash5495 -101 1 069Linear BGB = 0184P + 0575 007 078 075Power BGB= 0084P1125 306 099 075

Table 19 Generated TTB from developed equation using DBH

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM128 1295594 139 1474242 186 2336786 303 518241424 418944 1 6674 17 20251 298 50404221 6674 92 7725136 91 7593304 1 66741 6674 1 6674 188 2377058 44 221838444 2218384 1 6674 146 1592514 265 414892154 173205 135 140826 185 231676 1 667416 183976 1 6674 25 502 1 667410 8806 16 183976 16 183976 1 667410 8806 3 9282 194 2499618 16 18397613 132742 154 173205 108 9933456 18 221772128 1295594 215 294922 153 1714354 135 140826209 2817486 17 142064 128 1295594 1 667422 255016 122 1201862 162 1876246 148 162696219 241762 8 61912 209 2817486 175 212052 094 876 7150521 19 241762 16 18397689 7331824 13 132742 22 255016 15 1661714 371576 1 6674 78 5945736 185 23167612 520944 1 6674 52 3019696 14 149092165 193152 1 6674 45 2316 165 193152126 1264058 15 2958 45 2316 126 1264058153 1714354 1 6674 24 418944 153 171435413 132742 2 094 42 2025336 1 6674118 114083 97 8395216 51 2916984 13 13274214 371576 96 8259744 25 502 118 11408333 1192656 122 1201862 45 2316 145 1575415 2958 87 7073256 54 3227304 171 20440342 094 83 6564856 26 585784 1 66741 6674 109 1007766 1 6674 1 6674171 2044034 68 4762096 1 6674 18 221772171 2044034 69 4877184 9 74622 1 6674

12 International Journal of Forestry Research

Table 19 Continued

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM9 74622 29 841504 105 95052 124 1232814114 1080962 1 6674 46 2414344 114 1080962108 9933456 51 2916984 1 6674 108 993345611 102226 11 102226 1 6674 93 7857696105 95052 1 6674 1 6674 118 11408312 11712 12 11712 1 6674 156 17676627 4993 104 9363904 1 6674 7 4993122 1201862 52 3019696 7 4993 175 21205111 1036826 111 1036826 53 3123136 144 155835813 132742 61 3976864 13 446624 118 11408310 8806 1 6674 18 064104 10 8806128 1295594 128 1295594 1 6674 13 13274220 26248 68 4762096 1 6674 8 619121 6674 1 6674 1 6674 138 1457638104 9363904 1 6674 1 6674 114 108096214 149092 1 6674 98 8531416 154 17320516 183976 104 9363904 1 6674 84 6690864195 25203 62 4086856 1 6674 78 594573681 6315024 95 8125 28 755536 225 3174656 3437824 85 68176 49 2713744 1 667452 3019696 65 44212 42 2025336 156 176766210 8806 81 6315024 121 1186494 1 667413 132742 1 6674 87 7073256 1 6674169 2006238 1 6674 56 3437824 29 84150421 283926 82 6439576 1 6674 136 142464621 283926 57 3544176 15 16617 164 191302213 132742 1 6674 202 266711 1 667439 1741224 6 38676 297 5012242 1 6674173 2082122 1 6674 195 25203 17 2025116 183976 1 6674 23 329002 16 18397616 183976 1 6674 23 336616 187 235688621 283926 64 4309024 183 2276926 104 9363904187 2356886 48 2613216 12 11712 122 120186239 1741224 1 6674 54 3227304 13 132742132 1359538 1 6674 132 1359538 18 22177218 221772 1 6674 2 094 1 667458 3651256 15 2958 1 6674 1 6674

36 Biomass Stocks amongAgroecological Zones Based on theallometric equations the average TTB for G robusta treesgenerated in each of the AEZ studied is as shown in Table 9The TTB stock for each AEZ was 13 926 tonhaminus1 13109tonhaminus1 10869 tonhaminus1 and 11827 tonhaminus1 in UM1 UM2UM3 and UM4 respectively Variability of tree biomassbetween the four agroecological zones showed no significantdifference (p-value gt 005) implying that though there couldbe a slight difference in the allometry of the tree speciesamong AEZ the total biomass does not vary This alsoexplains that the management of G robusta trees in the

agricultural landscapes of the four AEZ does not differ andthe farmers can form a marketing unit despite their differentAEZ and their production quotas can be the same

The average biomass stock of 1243 tonha in the studycompares well with the findings of Albrecht [20] 2-22tonha Henry [1] 9ndash11tonha and Kuya [5] 16 tonhaall of which are for agricultural landscapes This findinggives a better glimpse of the tree component in agricul-tural landscapes and is a good guide for the develop-ment of carbon stock factors in agricultural landscapes[21] With this moderate stock the farmers are able to

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

12 International Journal of Forestry Research

Table 19 Continued

UM 1 GEN UM 2 GEN UM 3 GEN UM 4 GENDBH BIOM DBH BIOM DBH BIOM DBH BIOM9 74622 29 841504 105 95052 124 1232814114 1080962 1 6674 46 2414344 114 1080962108 9933456 51 2916984 1 6674 108 993345611 102226 11 102226 1 6674 93 7857696105 95052 1 6674 1 6674 118 11408312 11712 12 11712 1 6674 156 17676627 4993 104 9363904 1 6674 7 4993122 1201862 52 3019696 7 4993 175 21205111 1036826 111 1036826 53 3123136 144 155835813 132742 61 3976864 13 446624 118 11408310 8806 1 6674 18 064104 10 8806128 1295594 128 1295594 1 6674 13 13274220 26248 68 4762096 1 6674 8 619121 6674 1 6674 1 6674 138 1457638104 9363904 1 6674 1 6674 114 108096214 149092 1 6674 98 8531416 154 17320516 183976 104 9363904 1 6674 84 6690864195 25203 62 4086856 1 6674 78 594573681 6315024 95 8125 28 755536 225 3174656 3437824 85 68176 49 2713744 1 667452 3019696 65 44212 42 2025336 156 176766210 8806 81 6315024 121 1186494 1 667413 132742 1 6674 87 7073256 1 6674169 2006238 1 6674 56 3437824 29 84150421 283926 82 6439576 1 6674 136 142464621 283926 57 3544176 15 16617 164 191302213 132742 1 6674 202 266711 1 667439 1741224 6 38676 297 5012242 1 6674173 2082122 1 6674 195 25203 17 2025116 183976 1 6674 23 329002 16 18397616 183976 1 6674 23 336616 187 235688621 283926 64 4309024 183 2276926 104 9363904187 2356886 48 2613216 12 11712 122 120186239 1741224 1 6674 54 3227304 13 132742132 1359538 1 6674 132 1359538 18 22177218 221772 1 6674 2 094 1 667458 3651256 15 2958 1 6674 1 6674

36 Biomass Stocks amongAgroecological Zones Based on theallometric equations the average TTB for G robusta treesgenerated in each of the AEZ studied is as shown in Table 9The TTB stock for each AEZ was 13 926 tonhaminus1 13109tonhaminus1 10869 tonhaminus1 and 11827 tonhaminus1 in UM1 UM2UM3 and UM4 respectively Variability of tree biomassbetween the four agroecological zones showed no significantdifference (p-value gt 005) implying that though there couldbe a slight difference in the allometry of the tree speciesamong AEZ the total biomass does not vary This alsoexplains that the management of G robusta trees in the

agricultural landscapes of the four AEZ does not differ andthe farmers can form a marketing unit despite their differentAEZ and their production quotas can be the same

The average biomass stock of 1243 tonha in the studycompares well with the findings of Albrecht [20] 2-22tonha Henry [1] 9ndash11tonha and Kuya [5] 16 tonhaall of which are for agricultural landscapes This findinggives a better glimpse of the tree component in agricul-tural landscapes and is a good guide for the develop-ment of carbon stock factors in agricultural landscapes[21] With this moderate stock the farmers are able to

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

International Journal of Forestry Research 13

practice agricultural activities while maintaining a tree coverin the farms which stabilizes the agricultural landscapesand reduces pressure for wood products from adjacentforests

4 Conclusion and Recommendations

This study has developed a quick tool for estimating biomassfrom G robusta trees in agricultural landscapes of Maraguacounty The allometric equations allow better marketingof the trees and their components and will favor farmerswho will get better value from their trees The findingsillustrate no much variations in stocking among the studystrata and also comparing with studies in similar agriculturalsetups Therefore the study illustrates the usability of generalallometric equations which eliminate the expensive processesof destructive sampling As such the developed equationsare ideal for a wide range of application in areas of Kenyawhere G robusta grows without any need to develop otherequations

The study identified only small sized G robusta treesand the size limitation is influenced by their growth char-acteristics and the market conditions The study proposesa validation of the allometric equations in cases wherebigger sized trees exist Similarly the small sample sizeused in this study may have not captured enough infor-mation on the allometry of the tree and a collation ofthis data and other existing datasets can help comparecharacteristics of allometry that may influence the equationused

Appendix

A

See Table 10

B

See Tables 11 12 13 14 15 16 17 and 18

C

See Table 19

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Disclosure

The research was done as a part of a Masterrsquos thesis and wasfinanced by the first author

Conflicts of Interest

The authors have no conflicts of interest in the manuscriptsand therefore do declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge the Department of Nat-ural Resources in Karatina University where the studentis registered for providing supervision and guidelines Theauthors would also like to thank Kenya Forest Service (KFS)authorities for giving a permission to conduct the study usingtheir staff members and the farmers who allowed uprootingof trees in their farms

References

[1] M Henry P Tittonell and R J Manlay ldquoBiodiversity carbonstocks and sequestration potential in abovegroundbiomassin Smallholderfarming systems ofwestern Kenyardquo AgricultureEcosystems and Environment vol 129 no 1 pp 238ndash252 2009

[2] K P Acharya ldquoLinking trees on farms with biodiversity con-servation in subsistence farming systems in Nepalrdquo Biodiversityand Conservation vol 15 no 2 pp 631ndash646 2006

[3] P Daniel and K Michael ldquoEstimating carbon emissions fromforest degradation implications of uncertainties and areasizes for a REDD+ MRV systemrdquo Canadian Journal of ForestResources vol 42 Article ID 19962010 pp 1996ndash2010 2012

[4] B Verbist M Vangoidsenhoven R Dewulf and B MuysReducing Emissions from Deforestation and Degradation(REDD) KLIMOS Leuven Belgium 2011

[5] S Kuyah J Dietz and C Muthuri ldquoAllometric equations forestimating biomass in agricultural landscapes II Belowground-biomassrdquoAgriculture Ecosystems and Environment vol 158 pp225ndash234 2012

[6] M J Kinyanjui P Latva-Kayra P S Bhuwneshwar P KariukiA Gichu andKWamichwe ldquoAn inventory of the above groundbiomass in the mau forest ecosystem Kenyardquo Open Journal ofEcology vol 04 no 10 pp 619ndash627 2014

[7] J M Mugo J T Njunge and R E Malimbwi ldquoModels forpredicting stem diameter from crown diameter of open growntrees in sondu- nyando river catchmentrdquo Asian Journal ofAgricultural Sciences vol 15 pp 119ndash126 2011

[8] M Henry N Picard C Trotta et al ldquoEstimating tree biomassof sub-Saharan African forests A review of available allometricequationsrdquo Silva Fennica vol 45 no 3 pp 477ndash569 2011

[9] RMesquita J L Pereira andDe Souza State of the environmentMaragua District NEMA (National Environmental Manage-ment Authority) Nairobi Kenya 2004

[10] R Jaetzold H Schmidt B Hormetz and C Shisanya ldquoNaturalConditions and FarmManagement Informationrdquo in FarmMan-agement Handbook of Kenya Ministry of Agriculture NairobiKenya 2nd edition 2006

[11] J K Githiomi and D N Mugendi ldquoHousehold tree plantingand its relatedconstraints in meeting woodfuel productionin Kiambu Thika and Maragwa Districts of Central KenyardquoJournal of Horticulture and Forestry vol 4 no 7 pp 120ndash1252012

[12] S S Chauhan and J C FWalker ldquoVariations in acoustic velocityand density with age and their interrelationships in radiata

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

14 International Journal of Forestry Research

pinerdquo Forest Ecology andManagement vol 229 no 1-3 pp 388ndash394 2006

[13] J Chave C Andalo S Brown et al ldquoTree allometry andimproved estimation of carbon stocks and balance in tropicalforestsrdquo Oecologia vol 145 no 1 pp 87ndash99 2005

[14] J H Zar Biostatistical Analysis Prentice Hall Upper SaddleRiver 4th edition 1999

[15] J Glenday ldquoCarbon storage and emissions offset potentialin an East African tropical rainforestrdquo Forest Ecology andManagement vol 235 no 1-3 pp 72ndash83 2006

[16] J Pastor J D Aber and J M Melillo ldquoBiomass predictionusing generalized allometric regressions for some northeast treespeciesrdquo Forest Ecology and Management vol 7 no 4 pp 265ndash274 1984

[17] E T Mitchard S S Saatchi L J White et al ldquoMapping tropicalforest biomass with radar and spaceborne LiDAR in LopeNational Park Gabon overcoming problems of high biomassand persistent cloudrdquo Biogeosciences vol 9 no 1 pp 179ndash1912012

[18] F Rurangwa M J Kinyanjui F Bazimaziki et al ldquoDevelopinga Forest Management Plan (DFMP) for gatsibo district in theeastern province of Rwandardquo Open Journal of Forestry vol 8pp 247ndash265 2018

[19] V-L Benedicto A Carlos L J Jose OL-M Jorge G A CCristobal and G A Juan ldquoAllometric equations for estimatingbiomass and carbon stocks in the temperate forests of North-Western Mexicordquo Forests vol 8 no 269 2017

[20] A Albrecht and S T Kandji ldquoCarbon sequestration in tropicalagroforestry systemsrdquoAgriculture Ecosystems andEnvironmentvol 99 no 1 pp 15ndash27 2003

[21] IPCC Guidelines for National Greenhouse Gas Inventoriesvol 4 of Agriculture Forestry and Other Land Use TheIntergovernmental Panel on Climate Change 2006httpwwwipcc-nggipigesorjppublic2006glpdf4Volume4V4 04 Ch4 Forest Land

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