Proceedings—Research on Coniferous Forest Ecosystems—A symposium.Bellingham, Washington—March 23-24, 1972

Theodolite surveying fornondestructive biomasssampling

Eugene E. Addor, BotanistU.S. Army Corps of Engineers

Waterways Experiment StationVicksburg, Mississippi 93180

Abstract By theodolite surveying, the relative location of points in space may be calculated by triangulation. With the

aid of computers, data gathered by theodolite surveying may provide a dimensional analysis of individual trees.Because the system is nondestructive, the rates and patterns of change in the spatial structure of trees and standsmay be monitored by repetitive surveying. This paper presents a preliminary test of the approach upon trees in a40-year-old Douglas-fir (Pseudotsuga menziesii) plantation in western Washington. From experience gained inthe initial experiment, recommendations are made to increase the precision of repetitive measurements_

IntroductionThe theodolite is an instrument used in pre-

cise surveying to locate points in space by tri-angulation. The use of high speed computersfor converting angle measurements to pointlocations allows theodolite surveying tech-niques to be used for describing the physicalstructure of vegetation assemblages in con-siderable detail with relative ease. Such a sur-veying procedure has been used to constructsimulation models for studying the effects ofvegetation on engineering activities (West etal. 1971). Since the method is nondestructive,it offers the possibility of repetitive samplingwith high inherent precision. Exploratorysurveys were made recently to test the appli-cability of the system for this purpose (Westand Allen 1971). This paper examines somedata from a Douglas-fir stand at the Conif-erous Biome intensive site in Washington.

Description of theSurveying System

The procedure requires two theodolitesplaced at an arbitrary distance apart and lo-

cated conveniently to the subject trees (fig.1). The vertical and horizontal angles fromeach instrument to every point located in thesample space are measured with respect to abase line. The instruments can be movedabout to obtain clear lines-of-site to desiredpoints in the sample space and every instru-ment location (turning point) is referenced tothe base line by conventional traverse survey-

Figure 1. Instrument set-up for surveying spatialstructures of trees. Two theodolites are in use; theinstrument in the middle is a spotting laser.

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Figure 2. Graphic display of point location data from a Douglas-fir tree near Seattle, Washington, on whichbranching was not surveyed in detail. Bole graphed to show diameter to scale.

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ini; methods. Every point in the sample space:s thus located with respect to any arbitrarilylefined three-coordinate system. Details oftile procedure are presented elsewhere (Westand Allen 1971).'

One of the theodolites is equipped with aspecially designed circular reticle for measur-ing branch or stem diameter, employing theprinciple of stadia measurement. All measuredangles and reticle readings are recorded in thefield on specially designed data forms, andtrigonometric conversions of field data topoint locations and stem or branch diametersare made by computer. Figure 2 is an exampleof a computer graphic of one of the trees onthe Thompson site.

Description of the SampleThe Douglas-fir stand, located on the A. E.

Thompson Research Area in the Cedar Riverwatershed, lies some 64 km southeast ofSeattle, Washington. The Research Area isdescribed in detail by Cole and Gessel (1968).Measurements were obtained from a group ofeight contiguous trees on each of two proxi-mate (not contiguous) permanent researchplots (designated 1 and 2 on the Research.area) within an even-aged 40-year-old planta-tion. Plot 1 received three applications ofnitrogen as ammonium sulfate (NH 4 ) 2 SO4 atthe rate of 222 kg/ha in October 1963,October 1964, and May 1970. Plot 2 was leftuntreated as a control.

The eight trees selected for measurementon each plot were selected first by choosingan arbitrary point within each plot, and thentaking the eight trees nearest to each point assampling trees. The only controlling criterionplaced upon location of the starting point oneach plot was that it should be far enoughwithin the plot to avoid inclusion of bound-ary trees in the sample. Measurements on thesample trees were made in April 1970, beforebud burst, and then again in October 1970,after the apparent end of the growing season.

1 E. E. Addor and H. W. West. A technique formeasuring the three-dimensional geometry of stand-ing trees. U.S. Army Waterways Experiment Station,Vicksburg, Mississippi. Unpublished.

Data were taken to include the coordinatelocation and the diameter (outside hark) atthe following points:

At the base of the tree, defined as beingat the duff line or ground line, as wellas could be determined. Diameters weremeasured with a tape.Diameters at breast height (d.b.h.)150 cm above the duff line weremarked with a ribbon for subsequentremeasurement.The bole at every fourth whorl wherelimbs were still present (diameters werecalculated from reticle readings).The base of the live crown, defined asthe lowermost whorl at which morethan 50 percent of the branches heldgreen leaves. The location of a whorl isdefined as the approximate centroid ofbranch emergence; diameter measure-ments on the bole are made just belowthe lowermost branch as well as justabove the uppermost branch of thewhorl (fig. 3). (Diameters calculatedfrom reticle readings.)At every fourth branch whorl withinthe live crown, or at least one branchwhorl within the middle one-third ofthe live crown.The topmost whorl in April and thatsame whorl plus the new topmostwhorl in October.

g) The top of the leader, at the base of theterminal bud whorl.

Figure 3. Definition of branch whorl location, andlocation of diameter measurements at whorl.

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h) Point locations and diameters weremeasured for various defined points oncrown branches but will not be dis-cussed here.

A total of 30 turning points (instrumentset-ups) were established for the April surveyand all were referenced to a common coordi-nate system. The same points of referencewere used again in October, but no deliberateattempt was made to duplicate the surveyingsequence, e.g., to site each point on the treeand to measure each diameter from the sameturning point. Nonetheless, the sequence thatwas adopted for the first survey was approxi-mated during the second survey, as a result ofconstraints within the stand. Thus thesampled points were mostly viewed from thesample angles during both surveys. Since bothsurveys were referenced to the same coordi-nate system, the reported coordinate loca-tions of surveyed points are in theory exactlycomparable, so that any difference in thereported location of a point represents a dis-placement of that point by wind action,growth, or survey error.

Results ofTheodolite Survey

Crown Cover and Stand Density

The crown cover was essentially closed andthe branching structure relatively dense. Theground area occupied by the eight sampledtrees on each plot was determined in April bytraversing the ground points representing theouter crown limits of the outermost trees ofthe group. The crown coverage so determinedwas 31.2 m2 on plot 2 (unfertilized) and44.0 m2 on plot 1 (fertilized) representing acrown area per tree of 3.9 m 2 and 5.5 m2,respectively, or a density of approximately2,567 and 1,818 trees per hectare.

In this same stand, in October, 1965, Dice(1970) destructively analyzed 10 trees from a0.0045-hectare (45 m 2 ) plot, which is 4.5 m2per tree, or approximately 2,222 trees perhectare. These values lie reasonably between

our values for the unfertilized and fertilizedtrees. Unfortunately we are not certain howthe crown boundaries of his trees relate to theboundaries of his 45 m2 plot.

The problem of the true relation of thecrown cover per tree (tree mean area) tosample plot boundaries is controversial (Greig-Smith 1964). Supposedly, tree randomnesswith respect to sample-plot boundaries shouldbalance the excluded and included portions ofincluded and excluded trees, but the true rela-tion is apparently complicated by both plotsize and plot shape. A crown-limit traverse isrelatively simple with a theodolite survey andis easily converted to area by the computer. Itshould therefore be worthwhile to examinewhether such a procedure would resolve theproblem of the relation between sample plotboundary and tree crown boundary in thedetermination of crown cover, stand density,or tree mean area.

Patterns in Diameter Measurements

Examination of the diameter data from thetheodolite survey suggests that the unferti-lized trees exhibited greater increment on theupper portion of the bole than on the lower,whereas the fertilized trees showed approxi-mately equal growth pattern throughout thelength of the bole. Such patterns seem reason-able because of the difference in standdensity. Similar patterns have been reportedin unthinned and thinned stands of Douglas-fir surveyed with an optical dendrometer overa 2-year period (Groman and Berg 1971).

Certain sources of inaccuracies in diametermeasurements with the theodolite systemshould be mentioned. First, diameters calcu-lated from reticle readings are dependentupon accurate measurements of the distance.Second, interpolation errors from this sourcemay be important when estimating smallbranch diameters with the reticle. Counteringthese disadvantages is the possibility ofmeasuring diameter at any point on a stem orbranch regardless of the direction or angle ofinclination. Other instruments such as theoptical dendrometer have no reticle inscriptedand thus are restricted to measuring bolediameter.

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Patterns in Point. Displacement

Measuring changes in the physical structureof vegetation consists primarily of simplymeasuring the displacement of defined pointsover a specified time interval. Obviously, anerror in determining the location of a pointeither at the beginning or at the end of thetime interval will result in an error in themeasurement of displacement.

Measurement errors may stem from avariety of sources, depending upon themethods of measurement. Since theodolitesurveying is dependent upon calculation ofpoint locations by trigonometric relations,both instruments must be precisely sighted onthe spot to be located. Disparities in theassumed location of the target point willcause errors in the calculated location of thepoint. Horizontal disparities will cause hori-zontal and vertical errors according to theangle of convergence and the slope of lines-of-site, while a vertical disparity will not locate apoint at all.

To reduce errors from this cause, a spottinglaser (fig. 1) can be used to project a brightorange spot a few millimeters in diameteronto the tree at the selected target point. Thisprovides a definitive target for sighting thetheodolites at one given time, but it does notresolve the problem of relocating the exactpoint of measurement for periodic remeasure-ment. The spotting laser was at the ThompsonSite during both the April and Octobersurveys, but it was inoperable much of thetime. Periods of its use and nonuse mayaccount for some of the patterns in the data.

Other sources of error include the usualreading and transcription errors by instrumentmen and note keepers. Errors from thesevarious sources may or may not be critical,depending upon their magnitude and fre-quency, and the special purpose for which thesurvey is being made. For the purpose ofmonitoring subtle changes in the vegetationstructure over a brief time period, even verysmall errors may be important. Grossanomalies in the data may be identified andapproxiMately corrected during data editingand preliminary analysis, but small errorsregardless of source may not be distinguish-

able from true displacement.For the purpose of discussion, any dif-

ference between the calculated location of ade fined point from one observation toanother (specifically, for the present case,from April to October), in any coordinatedirection, may be defined as an "apparent dis-placement" of that point in that direction. Itcan then be defined that the apparent dis-placement always consists of two compo-nents : True displacement resulting fromchanges in the shapes of the trees, and errorsresulting from inaccuracies and mistakes ininstrument reading, note keeping, and calcula-tions. Hereinafter, these latter will be referredto collectively as "survey error." The questionto be resolved, then, is what proportion ofapparent displacement can be attributed toeach of these two components. Data from thesurveyed Douglas-fir stand provide anopportunity to examine the theodolitesurveying system with respect to theseproblems.

Figure 4 is a set of graphs of the apparentdisplacement in the xy (horizontal) plant ofdefined points at various levels on the treeboles, as measured from April to October.They are: (A) at the base of the tree, (B) atthe base of the live crown, (C) at an arbitraryintracrown whorl, and (D) at the whorl thatwas defined as the topmost whorl in April(i.e., at the base of the April leader, threetrees are omitted from the intracrown whorldata due to omissions in the survey). With fewexceptions, the apparent displacement in thehorizontal plane at the base of the tree iswithin plus or minus 3 cm, with a slight sys-tematic bias in the positive x direction and inthe negative y direction, but with the pointsfor the unfertilized and fertilized trees reason-ably well interspersed. Since trees areanchored at the base, it may be assumed thatany apparent displacement of the tree axis inthe horizontal plane at that level must repre-sent a surveying error. Therefore this slightsystematic error at this level on these treesmay be interpreted as a horizontal error inrelocating the established origin of the coordi-nate system. The absence of a separation inthis plane at this level between the apparentdisplacement of the unfertilized and fertilized

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Figure 4. Apparent displacement of the tree boles in x and y (the horizontal plane) at various levels on thesampled trees, from April to October: (A) at the base of the trees, (B) at the base of the live crowns, (C) atan intracrown whorl, (D) at the base of the April leader (based on data from table 2 in West and Allen 1971).

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trees indicates that the coordinate system wassurveyed across the intervening distance be-tween the two plots (about 20 m) with negli-gible error in this plane. If the data are ad-justed for the horizontal error in relocation ofthe coordinate system origin, then the dis-placement error is quite small, and it must beconceded that remeasurement of the hori-zontal angles to the trees has been achievedwith a fair degree of success, despite the 30turning points used in accomplishing thesurvey.

Two explanations may be suggested for theincreasing scatter of points in the horizontalplane with increasing height on the tree,shown on figure 4B, C, and D. First, it may beassumed that surveying errors have increasedwith increasing elevation of lines-of-site, orsecond, it may be assumed that the positionof the boles are less stable in the horizontalplane at higher levels on the tree. Since pointlocations in the horizontal plane are calcu-lated from horizontal angles, irrespective ofangles of elevation, there is no reason toassume that surveying errors should increasein relation to elevation. It follows thereforethat errors in the location of points in thehorizontal plane at any elevation might beequal to, but should not exceed, the errors inlocation of the base of the trees in this plane.It follows in turn that the apparent horizontaldisplacement of points on the upper boles ofthese trees must be a true displacement. Thepattern is consistent with what would beexpected as a result of movement of the treesby wind.

Figure 5 is a set of graphs of the apparentdisplacement of z (the vertical plane, or eleva-tion) for the same defined points on the bolethat are shown on figure 4, respectively.These show a considerable scatter in theapparent vertical displacement at the base ofthe live crown, moderate scatter in apparentvertical displacement at the intracrown whorl,and again a relatively close clustering ofapparent displacement at the base of the Aprilleader.

This pattern of variation may be attributedto relative differences in the difficulty ofidentifying the defined points with respectto elevation. This difficulty is more or less

inherent in the definition of the points; that isto say that "at or near the duff or groundline" is less definitive than is "the centroid ofthe branch whorl," whereas the topmostwhorl (base of the leader) is the smallest andmost definitive of the defined points. Thedifferences in vertical scatter of points for thebase of the live crowns and for the intracrownwhorl may be attributed to errors of approxi-mating the exact elevational location of thelatter through obscuring branches and foliage.These inconsistencies of identification haveimportant implications with regard to meas-urement of length relations, such as the totalheight of trees or the ratio of bole length tolength of live crown (although, of course, thesignificance of the implication is determinedby the magnitude of the dimensions and thespecial purpose for which the relations arebeing measured).

It was observed above that the apparentdisplacement of defined points on the unferti-lized and the fertilized trees were reasonablywell interspersed with respect to the hori-zontal plane. With respect to elevation, how-ever, the data exhibit systematic tendenciesthat require explanation. Specifically, figure5B shows a seemingly strong tendency towarda positive apparent displacement of about 6or 7 cm for the base of live crowns on thefertilized trees, while the apparent displace-ment of this point on the unfertilized treesappears to be randomly dispersed about zero.A possible explanation is that a vertical errorwas committed in extending the coordinatesystem across the distance (approximately20 m) between the two groups of trees. How-ever, if this were the case, then the sameapparent vertical displacement must occur atall other levels on the fertilized trees; if itdoes not, then its absence from other levelsmust be accounted for. The data for the intra-crown whorl (fig. 5C), though somewhatmore scattered than the data for the base oflive crown, do indeed suggest a similar dis-parity between central tendencies for the twogroups of trees, but a similar disparity is notobvious at the base of the trees (fig. 5A), norat the base of the April leaders (fig. 5D). Itmay be that for the base of the tree, the dis-parity is simply obscured by the scatter of the

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Figure 5. Apparent displacement of points on the tree boles in x and y as a function of z (elevation), from Aprilto October: (A) at the base of the trees, (B) at the base of the live crowns, (C) at an intracrown whorl, (D) atthe base of the April leader (based on data from table 2 in West and Allen 1971).

data; there is no obvious explanation for itsabsence at the base of the April leader.

ConclusionsThe preliminary survey of Douglas-fir trees

at the Thompson Site suggests that theodolitesurveying is adaptable to the purpose ofdetecting and monitoring subtle patterns ofchange in vegetation structures. In terms ofquantity and quality of data obtained for theenergy expended, this procedure appears tobe commensurate with any other known treemeasurement system, and it offers advantagesnot offered by any other system. First, be-cause the location of every point in thesample is determined relative to an arbitrarypoint defined as the origin of the coordinatesystem, the apparent displacement of anypoint on the tree is independent of theapparent location of any other point on thetree. Second, displacement of points in anydirection can be measured with this pro-cedure, such as, for example, the tips ofbranches radially disposed about the stem andgrowing at various angles from the vertical.Finally, and of considerable importance, thissystem is entirely nondestructive and is there-fore well suited to continued monitoring ofgrowth trends over extended time periods.

Theoretically, the precision of the tech-nique is within millimeters, since it is basicallythe same as is used for precision engineeringsurveying. There are, however, a few practicallimitations on the attainable precision.Following are a few observations about partic-ular problems.

A possible solution to the problem oftarget point identification would be to climbthe trees prior to the initial survey and affixpermanent sighting targets at points of in-terest. Also, a network of similarly smalldefinitive targets could be establishedthroughout the sample area for use as perma-nent reference points, one of which could beused to define the origin of the coordinate- ystem. A series of carefully controlled

periments should be designed specifically to! , , termine the effects of operator error on the_nuts of attainable precision under different

kinds of working conditions.Dense crown branches and foliage may

place constraints on the usefulness or con-venience of this method in some kinds ofvegetation.

When precision is required, surveyingshould be avoided during periods of adverseweather conditions. Tarpaulins can be sus-pended over the instruments so that workmay be carried on during rain or snow, butthese conditions also affect visibility withinthe forest. Winds that are strong enough tocause movement of the trees will obviouslyincrease the probability of meaninglessapparent displacements, and should beavoided.

As of this writing, the system has been usedexclusively for the dimensioning of trees. Theprinciples upon which it is based, however,are universally applicable mathematical rela-tions. Therefore the technique should beeminently suited to the study of a variety ofecological problems involving relations thatcan be described in a three-coordinate system.These might include, for example, the struc-ture of bird rookeries, the spatial arrangementof epiphyte or parasite plants, or flower andfruit distributions.

AcknowledgmentsThe work on which this paper is based was

authorized and financed by the Recreation andEnvironmental Branch, Office of the Chief ofEngineers, Washington, D.C., in cooperationwith the Coniferous Forest Biome, U.S. Analy-sis of Ecosystems, International Biological Pro-gram. This is Contribution No. 33 to theConiferous Forest Biome. I thank my referees,whose constructive criticisms were helpful inarriving at tenable explanations for some per-plexing patterns in the data.

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River research—a program for studyingpathways, rates, and processes of elementalcycling in a forest ecosystem. Univ. Wash.Coll. For. Res. Monogr. Contr. No. 4, 53 p.

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Dice, Steven F. 1970. The biomass and nutri-ent flux in a second growth Douglas-fir eco-system (a study in quantitative ecology).53 p. Ph.D. thesis on file, Univ. Wash.,Seattle.

Greig-Smith, P. 1964. Quantitative plantecology. Ed. 2, 256 p., illus. Washington,D.C.: Butterworths.

Groman, William A., and Alan B. Berg. 1971.Optical dendrometer measurement of incre-ment characteristics on the boles ofDouglas-fir in thinned and unthinned

stands. Northwest Sci. 45(3): 171-177. and H. H. Allen. 1971. A tech-

nique for quantifying forest stands formanagement evaluations. U.S. Army Eng.Waterways Exp. Stn. Tech. Rep. M-71-9,29 p., illus.

West, H. W., R. R. Friesz, E. A.pardeau, Jr.,and others. 1971. Environmental charac-terization of munitions test sites: Vol. 1,Techniques and analysis of data. U.S. ArmyEng. Waterways Exp. Stn. Tech. Rep.M-71-3, 31 p., illus.