A Simple Procedure for Mapping Tree Locations in

Forest Science,Vol. 35, No. 3, pp. 657-662 Copyright1989by the Societyof AmericanForesters

A SimpleProcedurefor Mapping Tree Locations

in Forest Stands DAVID D. REED HAL O. LIECHTY ANDREW

J. BURTON

ABSTRACT.A procedureis presentedfor mappingtree locationsdirectly into a Cartesiancoordinatesystemwithoutrequiringdistanceandbearingmeasurements in thefield. An independentcheck of the locationsof 401 trees by different field crews at different times showedthe methodto be both accurate(with an averagedifferencebetweenthe two measurementsof 0.01 m) and precise(with the standarddeviationof the differences being0.22 m). The methodis mostefficientwith a three-person crew. The time required to map a given area is dependenton tree density and visibility. In well-stocked(600 to 1100trees/ha)northernhardwoodstandsit is possibleto map I hectareper day with an experiencedcrew. The procedureis designedfor squareplots, but it can be adapted easily to circular plots. FOR. ScI. 35(3):657-662. ADDITIONALKEY WORDS. Spatial pattern, mapped stands,mappingprocedure, competition.

THE UTILITY OF SPATIALINFORMATIONwithin forest standshas been widely recognizedin ecologicalinvestigations,in studiesof intertree competition,

and in the developmentof distance-dependent tree growth models. Such dataare relativelyscarceandexpensiveto collectusingcommonprocedures (Oderwald et al. 1980). Most commonmappingproceduresuse measurementsof distancesandbearingsto individualtreesfrom commonpoints.The most accurate of these use a transit or staff compass,are time-consuming, and requiregreat care and well-trainedpersonnel.Even under the best conditions, relatively small errors in bearingsor distancescan result in large discrepancieswhen the measurementsare converted to Cartesian coordinatesof tree locations.Tradeoffsbetweensightinglong distancesand tying in multiple-sightinglocations are required. This paper presentsa simple methodthat usesinexpensiveequipment,is easy to train to field personnel, and is repeatableby differentcrewsat differenttimes. Someother mapping methodsmay be as fast, but an extensiveevaluation of these methodshas apparently not been reported in the literature. In the experience of the authors,no other methodresultsin the combinationof speed,accuracyand precisionof this method.

The authorsare, respectively,AssociateProfessorand ResearchScientist,Schoolof Forestry and Wood Products, Michigan TechnologicalUniversity, Houghton, MI 49931 and ResearchSpecialist,Departmentof Forestry,MichiganStateUniversity, East Lansing,MI 48824. This studywas supportedby fundsprovidedby the EasternHardwoodResearchCooperative withinthejoint U.S. EnvironmentalProtectionAgency/USDAForestServiceForestResponse Program and the U.S. Navy Space and Naval Warfare SystemsCommandthrough a subcontract with the IllinoisInstituteof TechnologyResearchInstituteundercontractnumberE0659588-C-001.The Forest ResponseProgramis part of the National Acid PrecipitationAssessment Program.This paper has not been subjectto EPA, Forest Service, or Navy peer review and shouldnot be construedto representthe policiesof theseagencies.ManuscriptreceivedAugust 10, 1988.

SEPTEMBER 1989/657

EQUIPMENT

The equipmentneededfor this procedureis relatively inexpensivecompared to equipmentneeded by the more common methods. In 1988, the equipmentlisted below couldbe purchasedfor lessthan $400 (US) from a numberof sources.The requiredequipmentincludes: ß ß ß ß

Two doubleright-angleprisms(also called "double pentaprisms") Two 50 m measuringtapes(the lengthis arbitraryand subjectto field conditions) Five 2 m rangepolesor straighthomemadepoles Disposablestring and flagging PROCEDURE

The mappingmethodworksbestwith a three-person field crew, but asfew as two peoplecan perform the work if necessary.The proceduredescribed below is for squareplotswith cornermarkersand a centerstake. Use of the double right-angleprismsallows mappingdirectly into a Cartesiancoordinate system.Theseprismshave three sightingviewfinders,which allow a field crew memberto locate a positionalongan existingline perpendicular to a point in the field. The initial step is to draw stringalong the plot boundariesbetween the corner stakes. Using the measuringtape, the center point of each plot boundaryis locatedand markedwith a verticalrangepole or flaggedstake. The measuringtapes are then stretchedbetweencenter pointson opposite sidesof the plot. This resultsin perpendicularplacementof the measuring tapeswith the tapesintersectingat the centerof the measurementplot. The tape placementshouldresultwith the tape zero pointson a plot boundary, the tape midpointsat the centerof the plot, andthe tape endpointson a plot boundary. The perpendicularityof the tapes is checked with the double right-angleprisms,andremeasurements or adjustmentsto the rangepolesor tapesare made as needed.If a tree or other obstaclemakesthis placement impossible,either or both tapes may be offset as long as they are perpendicular to each other and the zero points are on the plot boundaries. For each of the two measuringtapes, a crew member,equippedwith a doubleright-angleprism,takesa positionat the zero point of eachtape. The third crew membermovesfrom tree to tree within the plot, makingsurethat each tree is visited. At each tree, this third member uses a range pole or flaggedstaketo indicatea sightingpositionat the centerof the tree for each of the two crew membersalongthe measuringtapes. The crew membersat the measuringtapes move alongthe tapes and align the double right-angle prism with the tree of interest and the two range poles at the ends of the measuringtape (Figure 1). A weightattachedto the prismby a stringis used as a plumbbob to read the positionalongthe measuringtape. This givesa Cartesiancoordinateof the tree location in each direction which is recorded, alongwith the tree numberand otherinformationsuchas speciesor size, by the crew memberat the tree before movingto the next tree to be mapped. For plotswith a significantslope,measurements can be convertedto horizontal distanceusingtrigonometricrelationshipsfollowingmeasurementif the percentor angleof slopeis known. PERFORMANCE

The performanceof this mappingprocedureis illustratedusingdata from well-stocked(600-1100 stems/ha)northern hardwood stands. Locations of every tree on 18 individual50 m x 50 m squareplots were mapped.Loca658/FOREST

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N

0 R T H

RANGE POLES

9O

D I

90

90

R E

C T I O N

EAST

DIRECTION

FIGURE 1. Illustration of the field procedure.

tionsof every tenth tree in the center 30 m x 30 m area as well as the nearest tree to each plot comer, boundary midpoint, and comer of the 30 m x 30 m center area were remappedby different crews at a later time for each of the 18plots. This remappinginvolved a repeatof the entire procedure,including the placementof the measuringtapesanddeterminations of the plot boundary lines. The differencesin tree coordinates,in eachdirection,betweenthe original and the repeat mappingproceduresare used to evalute the performance of the procedure. Over the 18 plots, the locations of a total of 401 trees were remapped. Since each tree has two coordinates,this gave a total of 802 remeasurements. The resultsof the remeasurements(Table 1) indicate that the procedure is repeatablewith an averagedifferenceof 0.01 m between the original coordinates and the remeasured coordinates and a standard deviation

of

these differencesof 0.22 m. The results for the individual plots are more variable. When comparingamongthe 18 plots, large averagedifferencesand large average absolutedifferencesbetween the two measurementsaccompaniedby a typical standarddeviationindicatesthat the tape placementwas slightly(0.1 to 0.2 m) differentbetweenthe two measurements.This apparently happenedon plots 1, 2, 5, 6, and 17. Another sourceof error is in data recording.As can be seen in Figure 2, 82% of the measurementpairsdifferedby 0.2 m or less,and 91% differedby 0.3 m or less. There were several differences(9 out of 802) that were 1.0 m or larger. On revisitingsomeof theselarge differences,all were apparently causedby data entry errors during one of the measurements.These errors increase the standard deviation

of the differences

and can be due to either

SœYrœM•œa 1989/659

TABLE 1. Summaryof theperformanceof the mappingmethodson eighteen50 m x 50 m northern hardwoodplots. Average diameter

Plot

(cm)

No. of checked

Stems/ha

coordinates

Average

Average

D•

[al

SD

I

19.3

828

52

- 0.13

0.22

0.27

2

18.4

840

54

-0.12

0.18

0.22

3 4 5 6 7 8 9 10 11 12 13

18.8 19.9 21.2

800 772 652

-0.02 -0.02 0.11

19.3 16.9 18.5 19.2 19.6 19.8 22.7 20.8

900 1028 852 728 796 756 616 888

60 40 36 46 42 40 38 42 42 38 40

- 0.21 0.05 0.05 - 0.03 - 0.01 0.05 0.09 0.02

0.15 0.16 0.18 0.28 0.15 0.19 0.16 0.16 0.15 0.13 0.09

0.23 0.21 0.20 0.26 0.24 0.24 0.25 0.26 0.21 0.26 0.15

14

17.8

928

46

- 0.03

0.14

0.22

15

19.4

952

44

0.03

0.15

16 17 18 ALL

16.5 19.4 16.2 18.9

980 864 1104 849

48 44 50 802

0.07 0.10 -0.01 - 0.01

0.10 0.19 0.07 0.16

0.23 0.20 0.22 0.10 0.22

Originalcoordinate- remeasuredcoordinate.

the transpositionof numbersor misentry on the electronicdata recorder usedin the study. An occasionalplot (plots 13 and 18, for instance)with an averagedifferencenear zero accompaniedby low averageabsolutedifferencesand low standarderrorshad very consistenttape placementand very few data recording errors.

On the 50 m x 50 m plotsusedhere, the tapesintersectedat the plot center andresultedin tree locationsbeingup to 25 m from the measurementtapes. The measurements at all distancesfrom the tapesappearto be unbiasedas indicatedby averagedifferencesbetweenthe two measurementsbeingnear zero (Fable 2). Precision,as indicatedby average absolutedifferencesand the standarddeviation of differences, appears to decreasewith increased distancefrom the measurement tape.The crewmembersalsoreportedsome difficulty at short distancesbecausethe rangepole at the tree center appearedmuch largerin the viewfinderof the right angleprism than the two range poles along the measurementtape at the plot boundaries.This could have causeda slightincreasein standarddeviationwhen sighting0-5 m as indicatedin Table 2. There appears,therefore,to be an optimal sighting distancedue to the limitationsof the right angleprisms,which seemsto have been between 5 and 10 m for these plots. Similar problems with the viewfinder can occur when near a rangepole at one end of a measurementtape and far from the one at the other end. This, alongwith the generaldifficulties of sightinglong distances,contributesto the decreasedprecisionat longer distancesfrom the measurementtape. SUMMARY

AND

RECOMMENDATIONS

The methoddescribedin thispaperprovidesa procedurefor mappingtree locations in forest standsthat does not require expensive equipmentor 660/FOREST

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TABLE 2.

Summaryof differencesbetweenthe two observationsby distancefrom

the measurement tape. Sighting distance

No. of checked

(m)

coordinates

Average

Average

D•

I DI 0.13 0.12 0.14 0.16 0.26

0-5

224

- 0.00

5-10 10-15 15-20 20-25

119 216 119 124

- 0.03 -0.01 0.00 0.00

0.20

0.16 0.20 0.25 0.37

Originalcoordinate- remeasuredcoordinate.

speciallytrained field personnel.The procedureis repeatableby different crewsat differenttimesand, while other mappingproceduresmay be as fast or as accurate, provides a combinationof speed, accuracy, and precision that the authorshave not found in any other method. Following the evaluation of the proceduredescribedhere, there are severalrecommendations that can further reducethe time requiredto map a standand possiblylead to increasedaccuracyand precisionin the tree coordinates. 1. Mappingis most efficientin the springand fall when brushis at a minimum.In standswith a heavyunderstory,it may be necessaryto dividea plot into subplots (such as four quadrants)to expedite sighting.This requiresrelocation of the measurementtapes and careful record-keepingof the location coordinates mappedin the differentsubplots.Tape relocationmay alsobe requiredby steep terrain, complextopography,or very densestands. 2. Accuracyandprecisionnearthe plot boundariescanbe improvedby locatingthe rangepoles or flaggedstakesmarkingthe boundarymidpoints2 to 5 m outside of the plot while maintainingthe alignmentwith the measuringtapes.This would give a longersightingdistanceto the rangepolesor flaggedstakeswhen working alongthe measurement tapesneartheplot boundaryandpossiblyeliminatesome of the problemswith the viewfinderof the right angleprisms.Locatinga range pole or flaggedstake at plot center could also reduce the difficulty with long sightingdistancesand lead to increasedprecisionnear the plot boundaries. 3. To ensurethat eachtree is mappedandto increasethe speedof mapping,number or tag each tree on the plot prior to the mappingprocedure.While conductingthe mappingprocedure,a visualcheckcan then be madeto ensurethat no trees are inadvertentlyomitted from the map. In this study, the trees were numberedon all 18plotsprior to mapping;duringthe mappingprocedure,severaltreeswere identifiedthat had been missedduringthe initial numbering. 4. The methodspresentedhere can be easily adaptedto circular plot configurations. Prior numberingof trees is especiallyhelpful, but not required, when mappingcircular plots. Many electronicdata recordershave the capability of checkingif a tree'slocationis a greaterdistancefrom the plot centerthanthe plot radius,thusallowingplot boundariesto be determinedduringthe mappingprocedure.When mappingin circularplots, the measuringtapesare placedperpendicularto each other, intersectingat the centerof the plot, with the zero points on the plot boundary.Followingthe field work, if the centerof the circularplot is desiredto coincidewith the origin of the coordinatesystem, the value of the coordinatesfor the center point can be subtractedfrom each of the mapped locations,thus relocatingthe origin of the coordinatesystemat plot center. LITERATURE

CITED

ODERWALD,R. G., W. B. STUART, and K. D. FARRAR.1980. The Forest Model File: A mappedstandlibrary at Virginia Tech. For. Sci. 26:193-194.

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