Computer reduces cruise-data compilation errorhttps://scholarworks.sfasu.edu/texas_forestry_papers/1005/thumbnail.jp

Baker, Robert D.

Hunt, Ellis V., Jr.

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Stephen F. Austin State UniversitySFA ScholarWorksTexas Forestry Papers, No. 1-29, 1970-1976 Journals10-1970Texas Forestry Paper No. 4Ellis V. Hunt Jr.Stephen F. Austin State UniversityRobert D. BakerStephen F. Austin State UniversityFollow this and additional works at: http://scholarworks.sfasu.edu/texas_forestry_papersPart of the Other Forestry and Forest Sciences CommonsTell us how this article helped you.This Book is brought to you for free and open access by the Journals at SFA ScholarWorks. It has been accepted for inclusion in Texas Forestry Papers,No. 1-29, 1970-1976 by an authorized administrator of SFA ScholarWorks. For more information, please contact cdsscholarworks@sfasu.edu.Recommended CitationHunt, Ellis V. Jr. and Baker, Robert D., "Texas Forestry Paper No. 4" (1970). Texas Forestry Papers, No. 1-29, 1970-1976. Book 6.http://scholarworks.sfasu.edu/texas_forestry_papers/6TEXAS FORlSTRY PAPlR SCHOOL OF FORESTRY STEPHEN F . AUSTIN STATE UNIVERSITY Nacogdoches, Texas I' ' . ' ' ' 'I • I \ ' : 1 • ~~ . '. ' . . {• I \·, .. I •• ; ' .: '. ' .• ' l. ' .. ,., ,if ' . ' • ~ • . " . ' I ~ No.4 - OCTOBER 1970 COMPUTER R EDUCES CRUISE-DATA <.:OMPI LATIO N ERROR by EUis V. Hunt, Jr . and Robe.rt D. Baker1 Mensurationists hove long known that midpoint volumes applied to numbers of trees by one-inch or broader diameter classes generaJJy underestimate stand volumes. The errors stem primarily from two causes: I . The distributions within diameter classes may be biased in either direction. 2. Tree stem volume is proportional to the square of diameter rather than to diameter. The f11st cause may operate at random; the second tends always toward underestimation in ran-dom distributions. Because manual compilations are slow and costly, foresters have customarily economized by estimating and computing volumes by diameter classes, ignoring the resulting inaccuracy. Computer compilation now makes it feasible to avoid these errors. Development of a computerized plantation inventory program at SF A (Texas Forestry Paper No. 2. 1970) afforded an opportunity to evaluate the size of the errors resulting from using one-inch dbh classes. Stand volume for ten inventories of two stands near Nacogdoches were computed by both tenth·inch and one-inch diameter classes. Volume per acre computed through summarization by diameter to nearest tenth-inch was always larger than volume per acre computed through addition of the stock table arranged by one-inch dbh classes. The dif· ferences nveraged 2.4 percent. (Table 1) 1 Aulhort are, ru,.ctiwly, A...Uitnt Prore.saot and Pro restOr, School of Forestry, Stephen f', A Ullin State Unlwrahy. Both computations employ the same relationships between volume and dbh. The first compiled the volume for each sample tree, based on its d bh measured to the nearest tenth-inch. The second, or stock table method, computed the number of sample trees within each one-inch d.iameter class, and applied to them a volume computed for the nominal midpoint of the class, as in the usual manual computation. As indicated above, tree volumes do not bear a straight-line relation to diameters, but are approximately proportional to diameter squared. In any group of trees the average of the squared diameters is always larger than the average diameter. In a diameter class withln which trees are evenly distributed by sizes, their average diameter will be close to the midpoint of the class. but diameter of the tree of average basal area, or average squared diameter wiU be higher than the midpoint. The consistent bias revealed in Table I results from this mathematical rela· tionshlp. The percent difference. however. probably would be srnaUer for stands of larger dia· meter. Consider two theoretical diameter distributions, ( I ) a single tree in each tenth-inch class, and (2) ten trees at the midpoint of each inch class. The sum of squares of diameters of (I) wiU exceed that of (2) by 2.3 percent for the five·inch clas5. but by only 0.66 percent for the six· teen-inch class. Expansion of the squared diameters to volumes might somewhat magnify these differences because larger trees are also frequently taUer even within a one-inch dbh class. In conclusion, for young even-aged stands, one could expect volumes calculated by tenth-inch dbh classes to exceed those calculated by one-inch dbh classes by I to 4 percent. The error may be avoided at nominal cost by recording dbh measurements to the nearest tenth-inch and programming the computer to compile volumes on this basis. The printout from the SF A Plantation Inventory Program includes a summary, by one-inch classes, of numbers of trees and volumes computed in this way. Table I . A verage volumB pBr acrs from rsn cruisBs compurBd in rwo differsnr w1ys. N1cogdochts Ciry Planrarion, ssrablishsd 1942. Date of Inventory and Species I 96S 8 Slash pine' 196SA Slash pine' 1966 Slash pine 1967 Slash pine1 1968 Slash pine 19658 Lob1oUy pine' 196SA LobloUy pine' 1966 Loblolly pine2 1967 Loblolly pine 1968 LobloUy pine Computed from tenth-inch dbh classes Computed from one-inch dbh classes Cubic Feet 3204 3153 2047 201S 2186 2137 2940 2906 3038 2993 2620 2512 1727 1666 19SO 1873 2154 2112 2287 2247 l "8'" wu befote thlnnins, ,.A~· wu 1her thin nina wu complete. 'l In thl• 1nd •ubtequent years, a new vol·ume t1ble equation was uaed for thb ..,eclet. Difference P1rcenr 1.62 1.59 2.29 1.17 I. SO -4.30 3.66 4.11 1.99 1.78 

Texas Forestry Paper No. 4

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Texas Forestry Paper No. 4

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