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Diameter-based biomass regression models ignorelarge sapwood-related variation in Sitka spruce

B. T. BORMANN

Volume 20 • Number 7 • 1990

Pages 1098-1104

Printed in Canada / Imprime au Canada

e G

Purchased by USDA Forest Service for official use only

Diameter-based biomass regression models ignore large sapwood-related variationin Sitka spruce

B. T. BORMANN

USDA Forest Service, Pacific Northwest Research Station, 3200 Jefferson Way, Corvallis, OR 97331, U.S.A.Received September 13, 1989

Accepted February 2, 1990

BORMANN, B. T. 1990. Diameter-based biomass regression models ignore large sapwood-related variation in Sitkaspruce. Can. J. For. Res. 20: 1098-1104.

Precise estimates of biomass are needed in productivity and nutrient cycling studies, and for improved estimatesof potential productivity. Improvements in prediction of foliage and branch biomass were sought by comparing multipleregression models using stem diameter, sapwood radial thickness, and tree height as independent variables in standsof Sitka spruce (Picea sitchensis (Bong.) Carr.) in southeast Alaska. Five sites were sampled by stratifying trees intofour diameter and three sapwood-thickness classes. Within stands, sample trees with thick sapwood consistently had2-3 times more foliage and branch biomass than paired trees with thin sapwood but nearly equal diameter. Inclusionof both diameter and sapwood thickness in equations increased precision of foliage and branch biomass, leaf area,and net primary productivity by 15-31% and reduced standard error by 35-48% when compared with equations con-taining only diameter as an independent variable. Height growth over the last 30 years of intermediate and codominanttrees with thick sapwood was 12-27% greater than that of paired trees with thin sapwood but nearly equal diameterat breast height. The addition of total tree height to multiple regression models, however, had little effect on theirprecision. Stem biomass equations were not improved by including tree height or sapwood thickness. The use of adiameter - sapwood thickness sampling matrix for construction of biomass equations may reduce the sample size neededand result in equations with wider application.

BORMANN, B. T. 1990. Diameter-based biomass regression models ignore large sapwood-related variation in Sitkaspruce. Can. J. For. Res. 20 : 1098-1104.

Des evaluations precises de la biomasse sont necessaires pour les etudes de cyclage des elements nutritifs et de pro-ductivite ainsi que pour obtenir une meilleure evaluation de la productivite potentielle. Des ameliorations dans la predictionde la biomasse des feuilles et des branches ont ete obtenues en comparant des modeles de regression multiple qui utilisentle diametre de la tige, Pepaisseur radiale de l'aubier et la hauteur de l'arbre comme variables independantes dans despeuplements d'Epinette de Sitka (Picea sitchensis (Bong.) Carr.) du sud-ouest de l'Alaska. Cinq stations furent echan-tillonnees en stratifiant les arbres en quatre classes de diametre et trois classes d'epaisseur d'aubier. Dans un peuple-ment, les arbres a aubier epais echantillonnes avaient invariablement 2-3 fois plus de biomasse des feuilles et des branchesque les arbres a aubier mince auxquels ils etaient 'mires. Le fait d'inclure dans les equations a la fois le diametre etPepaisseur de l'aubier a augmente la precision, pour la biomasse des feuilles et des branches, la surface foliaire dela productivite nette, de 15-31% tout en reduisant l'erreur standard de 35-48% comparativement aux equations conte-nant seuiement ie ciiametre comme variable inciependante. Au cours des 30 dernieres annees, la croissance en hauteurdes arbres codominants et intermediaires a aubier epais a ete 12-27% plus forte que celle des arbres a aubier mincede meme diametre a hauteur de la poitrine auxquels ils etaient paires. Cependant, l'ajout de la hauteur totale de l'arbreaux modeles de regression avait peu d'effet sur leur precision. Les equations de biomasse pour la tige n'etaient pasameliorees par l'ajout de la hauteur de l'arbre ou de Pepaisseur de l'aubier. II est possible que l'utilisation d'une matriced'echantillonage selon le diametre et Pepaisseur de l'aubier pour la construction d'equations de biomasse reduise lenombre d'echantillons requis et permette de formuler des equations qui auraient une application plus large.

[Traduit par la revue]

1098

IntroductionConcepts of forest production, productivity, and poten-

tial productivity are changing as more concern is shown forlong-term site productivity, forest decline, climate change,forest insect-disease interactions, and nontimber resources.As a result, there is a greater need to quantify forest endproducts other than currently merchantable timber volumealone. Nonmerchantable biomass may be an importantresource by itself or may directly or indirectly influencefuture timber, wildlife, or water resources. Better measuresof potential forest productivity are needed to assess hownatural processes, management actions, air pollution, orclimate fluctuations can affect the sustainable productionof multiple resources and ecological values over the near andlong term.

Precise prediction of nonstem biomass and net primaryproductivity may only be achieved when we develop predic-tor variables that relate well to physiological function.Prediction of leaf area and weight can be based on a simple

pipe-model theory that states that transpiration, hence thearea of leaves, is related to the area of water-conducting sap-wood (Shinozaki et a!. 1964; Waring et a!. 1982). Precisemodels based on this idea have been constructed for westernUnited States conifers (Grier and Waring 1974; Kaufmannand Troendle 1981), Scot's pine (Whitehead 1978; Albrektson1984), red spruce and balsam fir (Marchand 1984), and oak(Rogers and Hinckley 1979). Few attempts have been madeto relate sapwood to tree parts other than leaves (Snell andBrown 1978; Makela 1986).

Traditional biomass equations that use only diameter atbreast height (DBH) have been constructed for many speciesto predict biomass components in forest stands (e.g.,Whittaker and Woodwell 1968; Koerper and Richardson1980; Grigal and Kernik 1984). Although many DBH modelspredict stem biomass precisely, relative lack of precision isobserved with foliage and branch components (e.g., Gholzet al. 1979; Grigal and Kernik 1984; Marshall and Waring1985). Many attempts have been made to improve predic-

Printed in Canada / Imprirne au Canada

BORMANN

TABLE 1. Characteristics of stands used to develop biomass equations

Stand

Mendenhallchronosequence

VankMl

M2 M3 Island Pavlof

1099

Avg. spruce DBH (cm)Min. spruce DBH (cm)Max. spruce DBH (cm)Avg. spruce SAP (mm)°Avg. spruce age (years)No. of spruce per hectareAvg. spruce height (m)Spruce site index

(m at 50 years)bSpruce basal area

(m 2. ha -1)Hemlock basal area

(m 2 -ha -1)Alder basal area

(m 2. ha -1)°Cottonwood basal area

(m 2. ha l)Total tree basal area

(m 2. ha -1)

9.5 11.7 37.4 31.2 33.3

3.0 3.0 10.1 3.2 7.5

26.1 42.1 68.0 77.7 66.8

22.7 13.9 15.5 23.8 21.4

46 90 178 66 100

3980 3640 1400 560 851

10.2 12.0 31.4 30.8 27.4

15.6 10.6 22.2 34.1 30.8

26.9 46.9 61.1 50.6 19.2

0.0 3.0 20.5 0.0 58.1

0.7 0.0 0.0 9.1 0.2

7.7 1.0 0.0 0.0 0.0

35.3 50.9 81.6 59.7 77.6

'Sapwood radial thickness at breast height./Tarr (1984).`Alnus sinuata in MI; A. rubra in Vank Island and Pavlof sites.

tion of nonstem components by including other predictivevariables like (DBH) 2 x height (e.g., Fujimori et al. 1976;Dickmann et al. 1985), using multiple regression models withheight, crown length, and other variables (Krumlik andKimmins 1976), or by using nonlinear models (Alban andLaidly 1982). The use of predictive variables in addition toDBH has had limited success especially when the additionaldifficulty and errors in measurement and poor linkage tophysiological processes are considered.

In this paper, I quantify the relation of DBH, sapwoodradial thickness, and tree height with components of sprucebiomass and productivity. I also compare the precision ofbiomass models that use DBH alone with those containingDBH and sapwood thickness or tree height and exploreconcepts of within-stand variation in tree biomass.

MethodsStand description and history

Five Sitka spruce stands were selected to represent an array ofage and site conditions in the northern half of the Tongass NationalForest (Table 1). A variety of stand types were representedincluding young, unproductive stands of Sitka spruce (Piceasitchensis (Bong.) Carr.) mixed with Sitka alder (Alnus sinuata(Reg.) Rydb.) and black cottonwood (Populus trichocarpa Torr.& Gray) on young glacial soils; older moderately productive sprucemixed with western hemlock (Tsuga heterophylla (Raf.) Sarg.);and a highly productive stand with spruce and red alder (Alnusrubra Bong.) developed after logging. All stands were naturallyregenerated and situated near sea level.

Three sites, Ml, M2, and M3, were established in the MendenhallValley, about 16 km north of Juneau, Alaska (58°16' N,134°30' W). These forest stands developed on glacial till depositedabout 70, 110, and 200 years ago, respectively, during the retreatof the Mendenhall Glacier (Chandler 1942; Crocker and Dickson1957).

The Pavlof site is near Freshwater Bay on the eastern side ofChichagof Island about 16 km northeast of Tenakee, Alaska(57°53 ' N, 135°10 ' W). The stand originated following a majorwindthrow event in about 1888 on alluvially reworked mixed glacialtill (Bowers 1987).

The Vank Island site is on small island that lies about 16 kmeast of Wrangell, Alaska (56°27'N, 132°41 ' W). This site waslogged in 1922 using track skidders that greatly disturbed soilhorizons. This was followed by a post-logging fire. These factorsprobably account for the presence of red alder (Harris and Farr1974). The importance of alder is declining in this 60-year-old standas alder is overtopped by spruce.

Tree selectionSample quadrats were 0.05 to 0.20 ha with a minimum of

50 spruce trees per quadrat. Sample trees were selected from withinthese quadrats to represent a wide range in both DBH and sapwoodradial thickness at breast height (sAP). From measurements of DBHon all trees in a quadrat, a mean (X), standard deviation (SD),and four diameters, specifically targeted for sampling, werecalculated. Target diameters, roughly corresponding to the crownclasses suppressed (sup), intermediate (INT), codominant (coDoM),and dominant (Dom), were calculated as follows: X - 1 SD; X;X + 1 SD; and X + 2 SD, respectively. The SAP was measuredon the six trees with DBH's closest to each of these DBH targets.Because most biomass in the stand was thought to be containedin trees with DBH'S close to INT and CODOM diameters, two fromeach of these groups of six trees, with the thickest and thinnestSAP, were selected. Trees were stratified in this manner to com-pare biomass on trees having nearly equal diameters but differentSAP. In the SUP and DOM classes, a single tree was selected closestto the mean SAP of the group of six closest to the DBH target.Thus, six trees in all were sampled from each stand, two INT andCODOM and one SUP and DOM.

Sapwood is easily identifiable in Sitka spruce by its greatertranslucency and moisture content relative to heartwood. Iodinedyes verified visual identification procedures. Two to three short

ThickM. Sapwood

3.0X1.3 X

5.7X

2.2X 1.1X 1.7X1.0X50 -

ThinSapwood

250

200 -

150 -

100 -

4.6X

1100

CAN. J. FOR. RES. VOL. 20, 1990

Foliage Biomass (kg/tree)

M1-I M1-C M2-I M2-C M3-I M3-C LP-I LP-C VI-I VI-C

Branch Biomass (kg/tree)

M1-I M1-C M2-I M2-C M3-I M3-C LP-I LP-C VI-I VI-C

FIG. Foliage and branch biomass on sample trees with nearlyidentical DBH but different sapwood radial thickness (sAP).Numbers above the thick-sAP class bars are the ratio of the thick-to thin-SAP class pair. The first two characters below each bar arethe site abbreviations (Mendenhall sites are M1-M3, VI is VankTcland , and PAV is Paldn); the third letter reprecentc either anintermediate ( I) or codominant (C) DBH class.

increment cores were extracted at breast height from trees at 120°angles and averaged. Sapwood radii were generally quite constantaround the stem in these trees.

Sample collection and processingThe six sample trees selected in each quadrat were felled, and

the live crowns were divided into five equal parts. All branchesin a tree were measured for their basal diameter and distance fromthe terminal and were classified as whorl or internode branches.A single branch not damaged during felling was randomly selectedfrom the middle of each crown fifth. Branches were divided intosix components; current year foliage and branches (woody por-tion); last year foliage and branches; and older foliage andbranches. Components were dried in the laboratory at 70°C to aconstant mass and weighed. For each sample branch, foliage andbranch biomass were calculated as the sum of all foliage and branchbiomass components, respectively. Sample branch data were usedwith a multiple regression model to predict total weight of branchcomponents per tree. Crown biomass was defined as the sum offoliage and branch biomass in the tree. Aboveground net primaryproductivity of spruce was estimated by adding weight of currentyear foliage and branch segments to weight of annual growth ofstems and branches. Annual growth of stems and branches wascalculated by multiplying current year stem volume increment(volume of current annual ring divided by volume of stem wood)by stem and noncurrent year branch dry weights (Whittaker andWoodwell 1968). Because many of these trees had not stopped

Ooco

Oqa-

OOcq

FIG. 2. Regression surface for foliage biomass as a function ofDBH and sapwood radial thickness. • , predicted foliage biomassvalues for sample trees used in the equation.

radial growth at the time of sampling, radial growth on the yearpreceding the current year was used with section lengths to calculatevolume increment.

Stems were also divided into five equal length sections andweighed in the field. A stem disk was taken from the base of eachof the five stem sections and at DBH. Disks were also weighed inthe field, returned to the laboratory, and oven-dried (70°C) tocalculate stem moisture content and total stem dry weight. Heightgrowth was reconstructed by identifying annual whorls and theirposition along the stem. Ring counts on sample disks were usedto verify whorl ages and to determine ages of positions along thestem below identifiable whorls. One-sided leaf area was determinedon fresh needle subsamples from each foliage age-class on eachsubsampled branch using a Li-Cor area meter (model LI-3000).1Samples were oven-dried (70°C) to determine leaf dry weight. Greenleaf area : oven dry weight ratios were multiplied by total foliagedry weight per branch to estimate total green leaf area.

No data on stem weight were collected on INT, CODOM, and DOMtrees on the Pavlof site and the one DOM tree on the M3 sitebecause trees were not felled. A modified rock climbing approach(Denison 1973) was used to collect branch data on these trees. Sap-wood thickness was inadvertently not measured on two trees lessthan 6 cm DBH (sup trees in M I and M2), resulting in a samplesize of 21 for stem and net primary productivity equations and 28for the remaining equations.

Model developmentBecause it was unfeasible to disassemble and measure all biomass

components of all branches within each sample tree, commonbranch equations were developed to predict foliage and branchweights of all branches in sample trees. Independent variables rep-resenting branches (diameter; position; and type, whorl or

'The use of trade names in this publication is for the informa-tion of the reader. Such use does not constitute an official endorse-ment or approval by the USDA of any product to the exclusionof others that may be suitable.

BORMANN 1101

TABLE 2. Comparison of the biomass model based on DBH alone (loge( Y) = 00 + 0 1 1oge(DBE)) with the multiple regression modelsDBH + tree height (THT; loge( Y) = 00 + 0 1 loge(DBH) + 13 2loge(THT)) and DBH + sapwood thickness (sAP; log e( Y) = 00 +

0,loge(DBE) + 02loge(sAP))

Model

Biomass component

olo change forDBH to DBH + SAPDBH DBH THT DBH + SAP

R 2 Sy, Sy, R2 Sr R 2 S,,Current-year foliage 0.71 0.14 0.72 0.14 0.90 0.08 26 - 40Last-year foliage 0.67 0.12 0.70 0.13 0.90 0.07 28 - 39Older foliage 0.82 0.13 0.83 0.13 0.95 0.07 15 - 46Current-year branches 0.71 0.13 0.71 0.14 0.88 0.09 24 - 35Last-year branches 0.77 0.12 0.77 0.12 0.94 0.06 22 - 48Older branches 0.80 0.13 0.81 0.13 0.92 0.08 14 - 34Stem biomass 0.97 0.05 0.99 0.04 0.97 0.06 0 1Net primary productivity 0.67 0.17 0.67 0.17 0.88 0.10 31 - 37Leaf area 0.79 0.15 0.80 0.15 0.95 0.08 18 - 46Foliage biomass 0.81 0.13 0.82 0.13 0.95 0.07 16 - 46Branch biomass 0.80 0.13 0.81 0.13 0.92 0.08 14 - 35Crown biomass 0.81 0.13 0.82 0.13 0.94 0.07 15 - 42

Model equations°

DBH alone DBH + SAP

Current-year foliage (cYF)Last-year foliage (LYF)Older foliage (PYF)Current-year branches (cYB)Last-year branches (LYB)Older branches (PYB)Stem biomass (STM)Foliage biomass (FoT)Branch biomass (BR)Crown biomass (cRwN)Net primary productivity (NPP)Leaf area (LEAF)

LCYF = - 7.752 + 2.323 X LDBHLLYF = - 6.614 + 2.128 X LDBHLPYF = -6.185+2.858 X LDBHLCYB = - 9.573 + 2.529 X LDBHLLYB = - 8.420 + 2.350 X LDBHLPYB = - 5.254 + 2.526 X LDBHLSTM = - 3.215 + 2.552 X LDBHLFOL = - 5.822 + 2.780 X LDBHLBR = - 5.1891 +2.518 X LDBHLCRWN = - 4.792 + 2.647 X LDBHLNPP = - 4.318 + 1.809 X LDBHLLEAF = - 2.820 + 2.336 X LDBH

LCYF = - 2.225 + DBH x 0.056 + LSAP X 0.725LLYF = - 4.270 + LDBH X 1.301 + LSAP x 0.780LPYF = - 1.799 + LDBH X 1.074 + DBH x 0.0355 + LSAP X 0.774LCYB = - 3.216 + DBH X0.0541 + LSAP x 0.678LLYB = - 6.068 + LDBH X 1.519 + LSAP X 0.793LPYB = - 3.702 + LDBH X 1.927 + LSAP x 0.782LSTM = - 3.215 + LDBH X 2.552LFOL = - 1.519 + LDBH X 1.022 + DBH X 0.0352 + LSAP X 0.773LBR = - 3.594 + LDBH X 1.907 + LSAP X 0.782LCRWN = - 2.906 + LDBH x 1.945 + LSAP X 0.823LNPP - 3.598 + LDBH x 1.469 + LSAP x 0.720LLEAF = - 2.567 + LDBH X 1.954 + SAP X 0.324 + LSAP X 0.394

NOTE: R 2 and Sy .„ are in logarithmic scale for both models and hence are directly comparabletree height units are metres, and leaf area units are square metres.

°Log-transformed variables are preceded by an L.

Biomass units are kilograms, DBH and sapwood thickness units are centimetres,

epicormic), trees (DBH; tree height (THT); and sAP), and stands(site index) were allowed to enter multiple regression equationsusing a stepwise procedure with an inclusion and exclusion p-valueof 0.15. R for these equations ranged from 0.75 for current-yearfoliage to 0.96 for older branches (unpublished data and equationson file, Forestry Sciences Lab, 3200 SW Jefferson Way, Corvallis,OR 97331). Data from every branch in sample trees were used withthese equations to estimate total dry weight of branch biomass com-ponents per tree.

A series of multiple regression models were constructed for entiretrees to compare biomass equations containing DBH, DBH and THT,and DBH and SAP. Appropriateness of assumptions necessary forregression analysis was evaluated graphically. A loge transforma-tion was always required for the dependent variables to linearizemodels and equalize the variance, making it possible to compareR 2 and standard errors of all equations (Payandeh 1981). Thedependent variables were selected in either their transformed oruntransformed state with a stepwise multiple regression procedureusing an inclusion and exclusion p-value of 0.15.

Results and discussionPaired Sitka spruce trees growing in the same stand with

nearly identical DBH'S but with variable sapwood thicknesshad remarkable differences in foliage and branch biomass(Fig. 1). Foliage and branch biomass of sample trees with

thick sapwood averaged 2.6 and 2.5 times greater, respec-tively, than their paired thin sapwood sample tree of nearlyequal DBH (p < 0.01; paired t-test). Alternatively, stembiomass was little affected by sapwood thickness. With dif-ferences of this magnitude, it is easy to understand (i) thedifficulty in constructing precise equations to predict foliageand branch biomass from DBH alone and (ii) the potentialfor bias in constructing equations using DBH alone based ontrees selected nonrandomly.

It is also therefore not surprising that SAP is a useful addi-tional independent variable in foliage and branch biomassequations. The R 2 of equations using the DBH-alone model,excluding that for stem biomass, ranged from 0.67 to 0.82(Table 2). This increased dramatically in DBH + SAP equa-tions to 0.88 to 0.95, a 15 to 311/4 increase. Net primary pro-duction and single-year growth components were mostimproved by the addition of SAP followed by foliage, leafarea, and older multiple-year foliage and branch compo-nents. The effect of SAP on the regression surface forfoliage, for example, is considerable, especially as DBH andSAP get larger (Fig. 2). Sapwood thickness did not improvethe DBH-based equation for stem biomass (p > 0.15), sug-gesting that vigor of individual trees did not greatly influencestem form.

40

E

30

0 20co(.7)

10

0

30

H 20co

10

0

1102 CAN. J. FOR. RES. VOL. 20, 1990

M1 M2 M3 VI

M1 M2

..,...

M3

1

. ..

— Thin SAP,---Thick SAP

VI

/c

..i

1940 1980 1900 1940 1980 1820 1860 1900 1940 1980 1940 1980

DateFIG. 3. Patterns of height growth in paired thick and thin sapwood radial thickness (sAP) class sample trees. Paired trees have nearly

identical DBH and are from intermediate (II) and codominant (III) diameter classes. Mendenhall sites are M1-M3 and VI is Vank Island.

l

a) 0.18

E 0.14

3 0.10'5)

0.06rnco.c 0.02

4)0 -0.02

ar -0.06

v -0.10w

0-10 10-20 20-30 30-40 40-50

Growth period (years before 1983)

FIG. 4. Average paired difference in height growth (thick minusthin sapwood thickness class trees) over the past five 10-yearperiods. Bars are 95% confidence intervals. Paired trees have nearlyidentical DBH and are from intermediate and codominant diameterclasses.

Inclusion of tree height in the model had little or no effecton the precision of biomass equations (Table 2). Tree heightappears to be a less sensitive indicator of current nonstembiomass than SAP because it is more of a cumulativemeasure that does not always reflect current conditions. Thisis also revealed in the complex and variable relationshipbetween SAP and tree height growth (Fig. 3). Differences intotal height and patterns of height growth developmentbetween paired thick and thin sapwood trees appeared tobe less consistent than differences in foliage and branchbiomass (Fig. 1). Trees with thick sapwood were taller insix of eight pairs of trees. In five of eight pairs, trees withthick sapwood had slower early growth that was maintainedor increased recently. Thick sapwood trees, however, didgrow 3-8 cm • year -1 (12-27 07o) more than their thin sap-wood pair during the last 30 years (Fig. 4). Beyond 30 years,

pairs had similar rates of height growth, which suggests thatcurrent sapwood thickness, and perhaps nonstem biomass,is related to how fast the tree has grown over the past30 years. Age of trees appears independent of current sap-wood radial thickness. Four of the eight pairs of trees withsimilar DBH had similar ages; in two pairs, the thick sap-wood tree was older and in the other two pairs, the thicksapwood tree was younger (Fig. 3).

Combined use of DBH and sapwood radial thickness hasseveral key advantages over the use of sapwood cross-sectional area. Measurement of sapwood thickness requiresone or more short increment cores where sapwood is directlymeasured. To nondestructively measure sapwood cross-sectional area, it is necessary to mesasure sapwood thicknessand either inside-bark radius with an increment core to thepith, or outside-bark radius from a circumference measure-ment minus bark thickness. Either way, some additionalerror due to an off-center pith or measurement of barkthickness should be expected. Also, sapwood cross-sectionalarea can mask important differences because a larger treewith a small sapwood thickness can have the same sapwoodcross-sectional area as a smaller more vigorous tree. Themost important advantage of separating sapwood area intosapwood thickness and DBH is the increased information onpossible age and site effects that allows for better modelapplication.

Individual sample trees were well dispersed in the DBH,SAP sampling matrix (Fig. 5), suggesting the possible needfor unique biomass equations for various combinations ofsite and age if the equations are a function of DBH alone.This dispersal reflects a wide range in site, age, and struc-ture among-selected stands (Table 1). Because SAP explainsa considerable amount of variation in foliage and branchbiomass, information on the dispersal of trees within a DBH,SAP matrix could help to reduce misapplication of equationsby defining the two-dimensional limits beyond whichextrapolation will occur.

10 20 30 40

DBH (cm)50 60 70

BORMANN

1103

FIG. 5. Distribution of sample trees in the DBH - sapwood thickness sampling matrix. Trees from a common site are encircled(Mendenhall sites are M I -M3, VI is Vank Island, and PAV is Pavlof).

ConclusionsWe should expect increased precision and applicability of

biomass models when predictive variables are included thatrelate in some causal way, dimensional or functional, to thebiomass of tree components. The DBH that represents twoof the three dimensions of stem volume adequately describesstem biomass, at least in trees that do not greatly differ inwood density or stem taper. Inclusion of THT, the thirddimension of stem volume, in addition to DBH did notappear to have any significant effect on the precision ofbiomass equations. Foliage, leaf area, branches, and current-year growth are less well represented by DBH alone orDBH THT. Sapwood thickness, a structural variable moreclosely related to physiological processes, should be con-sidered when constructing equations to predict these depen-dent variables.

Traditional models that predict nonstem biomass shouldbe questioned in light of the large variation in SAP andnonstem biomass not explained by DBH or DBH THT.Studies where traditional models have achieved high preci-sion for nonstem biomass may indicate less of a sapwoodeffect in that species, cultural practices that have reducedwithin-stand variation, a more limited range in climatic oredaphic conditions, or nonrandom sampling. The net pri-mary productivity estimation procedures using change innonstem biomass based on radial increment (Newbould1967) are dependent on the quality of the DBH-alone modelsand should also be questioned. While single-year estimatesof net primary productivity suffer from year to year climaticand other factors, they represent the only useful method ofestablishing ground truth in remote sensing trials or testsof other single-year measurement indices. New approachesare needed to incorporate sapwood thickness into multiyearnet primary productivity estimation procedures that perhapsinvolve the relation of sapwood thickness to ring pattern-ing or height growth.

Sapwood is easy to measure in many species with relativelylow measurement error. Sapwood, however, is not a usefulpredictor variable for some species, like western hemlock

where it is difficult to identify. It should also be recognizedthat because sapwood performs many important functions,including transport of water and nutrients, storage of carbo-hydrates, nutrients and water, and defense from insects anddisease, it may not relate closely to biomass in all situations.Sapwood-heartwood ratios may adjust to wind conditionsto provide necessary support (Long et al. 1981), and sap-wood permeability can also vary (Whitehead et al. 1984;Bancalari et al. 1987).

Additional understanding of tree to tree variation throughmeasurement of sapwood thickness could help reduceneeded sample size, better identify mean trees, and betterevaluate the applicability of equations for a site not includedin the sample used to construct the equation. This knowl-edge could also be incorporated into new intensive thinningstrategies that use diameter and sapwood thickness to iden-tify trees that are changing diameter, crown class, or rateof height growth.

AcknowledgementsThis work was carried out under sometimes difficult

logistical and weather conditions with adept field assistancefrom Robert Deal, Kirk Vail, Robert Haberman, and DaveBassett. Thanks are also due to W.A. Farr, P. Alaback,R.H. Waring, and the Associate Editor for their insightfulreview comments.

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