Merchantable-stem Green and Dry Weight Prediction Equations Based on a New Segmented-stem Taper Model
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1 Mernleem Green n Dry Weg Preon Euon Be on New Segmeneem Ter Moel Plnon Mngemen Reer Cooerve Dnel B. Wrnell Sool of Fore Reoure Unvery of Georg en, Georg 6 PMRC TECNCL REPORT 8 My, Comle y: Roer L. Bley Zxng Fng T yem of weg reon moel followu wor o e egmeneem er n volume yem reore y Fng, Borer n Bley n PMRC Tenl Reor 999.
2 Exeuve Summry Be on er meuremen n green n ry weg for lnongrown l Pnu ello Engelm. n lololly ne Pnu e L., new yem of mulneou er, volume n weg moel roue mrove fng wen ue o re ree volume n weg. Te ervolume moel from revou wor Fng, Borer n Bley omne w n euon for weg er un volume rove omle reon of green n ry weg o vrle o meer. Te reon for green n ry weg vry n logl relon w ge of e ree n ne ove e groun. Sunl mrovemen n of f over oe for ror PMRC moel re rele w ro o weg euon. Te ol moel rron n Borer 989 for mernleem ry weg fe w ee roue jue R vlue of.87 n.88 for lololly n l, reevely. Te ry weg reon moel n yem roue jue R vlue of.98 n.99 for lololly n l.
3 nrouon em o moel e form of n nvul ree e from e erly enury Bere 9, 97. Tey re rere y wo roe: exre vrle form ngle onnuou funon or exree vrle form w e funon n u wy e ole ere no egmen y nfleon on w form eng onn wn e egmen n fferen eween egmen. Exmle of o roe oun n e lerure. Tylly, of moelng log le o n euon form fe o er meuremen. Sueuenly, negrl lulu my e le o erve volume euon from e er moel. n ulrn erure from moel for em er, Burr 977 nroue e one of n euon o re volume o ny mernle o lm w o lm meer elf enerng reor vrle n e moel long w meer re eg n ol eg. euon llow one o re ol volume el e of mernle volume wen o meer eul ero. Followng wor, Cluer 98 owe u moel Burr 977 my e nlye ung e funmenl eorem of lulu o evelo n mle er euon. Reenly Fng e l. reene new exmle of e egmeneole ye of er moel gve exellen reul for lnongrown l Pnu ello Engelm. n lololly ne Pnu e L.. Te volume euon eveloe n wor lo e ly o re e volume o ny uerem meer or mernle eg for gven n ol ree eg w ol volume el e. Te ven of weg lng Tr 956 n e relon of mny vnge mule nere n ree meuronl moel for reng green n ry weg o vrou mernle o meer lm. Mo u euon rely re e weg o ome mernle o meer for gven nu of, ol eg, n e mernle o meer mu e me e vrleo volume euon oe. For exmle, rron n Borer 996 ue mlr form of euon for weg reon er moel for vrleo volume reon, w elf mlr o e vrleo volume moel nroue y Burr 977.
4 Prreol n Tom 989 nroue n logeer fferen ro o weg reon e on e one of e m of lmn w onnuou, onn eny. Worng w from l ne lnon, ey rove lner regreon euon o re ef grvy funon of relve eg.e. mernle eg ve y ol eg n ree ge. Tey lo fe e er moel of Ko e l. 969 w from lnongrown l ne ree. By negrng e rou of lmn me ef grvy over e lm n relve eg, Prreol n Tom 989 erve mernleem weg reon euon. Ojeve n nnovve yem for ervolume moel e on egmeneem w fferen form for for e egmen Fng e l. gven re o new nng regrng volumeer relon. owever, noe ove, e mer nury move wy from volumer meure n fvor of weg. Tu, our ojeve n wor w o exen e yem of Fng e l. o nlue vrleo weg reon omle n logl exenon of e yem. We were rulrly neree n e enynegrl ro of Prreol n Tom 989 n e vrleo weg reon euon reene y rron n Borer 996. We lo wne o exlore oer lernve, u rely reng e verge weg er f for vrle em egmen. Te For wor we ue weg from e me lololly Pnu e L. n l ne Pnu ello Engelm. e ere y Fng e l.. D were vlle from 8 nvul lololly ne ree one from 76 mle lo loe n lnon n e ol ln n emon yogr rovne of Nor Croln, Sou Croln, Georg, Flor n lm. Meuremen were vlle on 87 nvul l ne ree from 56 lnon lo n e ol ln of Georg n nor Flor. n mo e, four mle ree wou ny ovou em normle were felle on e mle lo. 4
5 5 Tree eleon n meuremen roool re ere y Fng e l.. Te emnly meuremen en 5f nervl on e em were ue n e overlngol meo Bley 995 o eermne oerve volume o vrle o meer. From en e um n e o of e ol, green n ry weg n l er f were eermne. fer ee lulon, ere were ol of,59 oervon vrle o lm for e ervolumeweg yem for lololly ne n 8,45 oervon for e l ne. For e lololly ne ree, ge verge 4 yer n rnge from 9 o 6; verge 6.5 n. n rnge from. o.6 n.; n ol ree eg verge 4 f n rnge from o 85 f. For e l ne mle ree, ge verge 5 yer n rnge from 9 o 7; verge 6. n. n rnge from.6 o.5 n.; n ol ree eg verge 45 f n rnge from 9 o 76 f. Te Tervolume Moel Te ervolume moel yem of Fng e l. n e ummre follow: m V were D,, /, e um eg ro;,
6 ,,,, f < { Oerwe, f { < Oerwe, /, n e Engl onn o onver n f no f. D meer re eg n., ol ree eg f, uerem meer n. eg, e leng f from groun o uerem meer, n n, re e leng f from groun o nfleon on n, n re orreonng eg ro. Eme for e oeffen n yem re, of oure, rove y Fng e l.. We wll no reen oe oeffen ere eue we ve refe e yem mulneou e of euon nlung weg moel omonen. We omre e fng of our new ervolumeweg yem o oe rng from fng e erweg moelng ro of Prreol n Tom 989 n e vrleo weg reon euon of rron n Borer
7 7 Weg Moel Comonen Smlrly o e ef grvy reon euon eveloe y Prreol n Tom 989, we yoee e followng moel:, were e verge l/f for e em egmen from um eg o ne f from e groun, e ree ge n yer, n,, re regreon oeffen o e eme w e. Of oure, e regreon oeffen eme wll e unue eenng on e reon of green or ry weg. One ee oeffen eme re nown, e weg reon euon re from e negrl of e er moel n euon : WT, were WT weg of ree em nlue eween e eg n. Suuon of e rore euon from ove roue ł Ł Sne ere re ree egmen for e er euon, e mernle weg one for ree n egmen: Segmen : f <, ł Ł ł Ł WT
8 8 Segmen : f <, ł Ł ł Ł ł Ł ł Ł WT Segmen : f WT Le:,
9 9,,,, n w ee n revouly efne erm, we n wre e mernle weg euon n om form: ł Ł WT 4 Sne e weg euon one y negrng e omle er euon, ll e roere of omly n e ervolume yem re reerve. Moreover, e reulng weg reon euon ner ee ne roere well. Fnlly, e omle ervolume weg moel yem e on reeegmen em er moel n e ummre follow: m V ł Ł WT / D V W Were: D meer re eg n., ol ree eg f., ree ge yr, uerem meer n. eg f., e leng f. from groun o uerem meer, n V ol ree volume f
10 W ol ree weg l. V m Mernle volume f o n uerem meer of W m Mernle weg l. o n uerem meer of e Engl onn, D, /, /,,,,,,,,,,,, f ol eg gven en: { f Oerwe <, { < f Oerwe f uer meer lm gven en: { D D f Oerwe <, { D f Oerwe < D, D
11 Prmeer Emon W e of e wo e of, euon,, n 4 were fe mulneou yem Borer 989 ung fullnformon mxmum leloo w nl rmeer eme rove y OLS n SUR. nl reul w unwege fng uggee reul oul e wege ung uerem eg of e nvul ol. n orer o ve e weg um o e numer of oervon, e weg ue were w /ol eg, were e onn eermne for e of e x e n volumeweg omnon o # oervon w eul e um of oervon. For e reulng x euon, ll roue remrly goo of f w e lowe jue R vlue eng.97 for e lololly ner er euon Tle 4. Plo of wege reul over ol eg owe no ren n unformy of vrne ro eg vlue. No relon eween wege reul n oer vrle were ren. n on, e eme for rmeer n euon ow logl ren. Pree ry woo eny eree < eg u e ree nree nng e effe of n nree erenge of juvenle woo were green woo eny nree < eg nree nng e effe of n nree n moure onen. Te relon on ree ge ne n nree < n ry weg eny w ge nve of ger rooron of le woo n, ene, ger ef grvy. Green weg eny ree o eree w ge. T woul ne e effe of ger moure onen for e younger ree offe e effe of ger ef grvy of woo n e oler ree. loug e ne effe mll.9 l/f /yr for lololly n.7 l/f /yr for l, no llogl.
12 Moel Comron Summry Tle 5 n 6 from fng e erweg moel of Prreol n Tom 989 n e vrleo weg reon euon of rron n Borer 996 ne very loe greemen n reon eween our yem n of Prreol n Tom. owever, ju Prreol n Tom, we foun e lmn negrl ro o evelong weg euon ueror o e vrleo weg reon moel. n our e, we ue e rron n Borer euon for omron. mlr n ruure o e weg ro ro Prreol n Tom omre er yem w. Summry Exenng e egmeneem form for yem of Fng, Borer n Bley o nlue rovon for reng weg logl nex e. By rng w relon eween eny green or ry n lner funon of em eg n ree ge, e lmn negrl ro nroue y Prreol n Tom 989 reul n euon for green weg oue r n ry weg ne r. Te yem f very well w from erere lololly n l ne lnon w reul re ueror o oe from fng vrleo weg euon.
13 Lerure Ce Bley, R. L Uerem volume from emnly : n overlng ol meo. Cn. J. of For. Re. 5:77. Borer B. E Syem of euon n fore n moelng. For. S. 5: Burr,. E Cufoo volume of lololly ne o ny mernle o lm. So. J. l. For. : 79. Cluer, J. L. 98. Develomen of er funon from vrleo mernle volume euon. For. S. 6:7. Fng, Z., B. E. Borer n R. L. Bley.. Comle volumeer moel for lololly n l ne e on yem w egmeneem form for. For. S. 46:. rron, W. M. n B. E. Borer Yel reon n grow rojeon for erere lololly ne lnon n e Croln, Georg, lm n Flor. S. Of For. Reoure, Te Unvery of Georg, en, G US. PMRC Tenl Reor Ko,., D.D. Munro n J..G. Sm Ter funon n er lon n fore nvenory. For. Cron. 45:788. Prreol, B. R. n C. E. Tom enynegrl ro o emng em om. For. Eology n Mg. 6: Tr, M Buyng ulwoo y weg omre w volume meure. U.S.D.. Fore Serv., SE For Ex S, S P 74,.
14 Tle. SS Syem of f for lololly ne erere lnon: ner meer, n., ner mernle volume MCVB, f, n ner ry weg MCDRYWT, l. Nonlner FML Summry of Reul Error DF DF j Euon Moel Error SSE MSE Roo MSE RSure RS MCVB MCDRYWT Prmeer Eme rox S Err Vlue rox Pr >. 9.E <. < < E <. < < <. < < <. <. Numer of Oervon,48 Tle. SS Syem of f for l ne erere lnon: ner meer, n., ner mernle volume MCVB, f, n ner ry weg MCDRYWT, l. Nonlner FML Summry of Reul Error DF DF j Euon Moel Error SSE MSE Roo MSE RSure RS MCVB MCDRYWT rox rox Prmeer Eme S Err Vlue Pr > < < <. < < <. < < <. < <. Numer of Oervon 8,44 4
15 Tle. SS Syem of f for lololly ne erere lnon: ouer meer o, n., ourer mernle volume MCVOB, f, n ouer green weg MCGRWT, l. Nonlner FML Summry of Reul Error DF DF j Euon Moel Error SSE MSE Roo MSE RSure RS o MCVOB MCGRWT rox rox Prmeer Eme S Err Vlue Pr > < < E <. < < <. < < <. < <. Numer of Oervon,6 Tle 4. SS Syem of f for l ne erere lnon: ouer meer o, n., ourer mernle volume MCVOB, f, n ouer green weg MCGRWT, l. Nonlner FML Summry of Reul Error DF DF j Euon Moel Error SSE MSE Roo MSE RSure RS o MCVOB MCGRWT Prmeer Eme rox S Err Vlue rox Pr > <. < < E <. < < <. < < <. <. Numer of Oervon 8,44 5
16 Tle 5. omron of f for ree moelng yem n er ly o re ne r ry weg f of lololly ne n erere lnon. ll ree moel fe w full nformon mxmum leloo ung SS. Reul were wege y ol eg. Moel # rm MSE roo MSE l. Men Re. l. S Re. l. Segmeneem moel 5.67 * rron & Borer Prreol & Tom * Sne 8 rmeer,,,,,, n re re y e omonen of er, mernle volume n mernle weg, n mulneou emon e numer of rmeer for oe oun 8/.667 n e omonen n e yem. So for e weg euon, e ol numer of rmeer,, n r R j. R Tle 6 omron of f for ree moelng yem n er ly o re ne r ry weg f of l ne n erere lnon. ll ree moel fe w full nformon mxmum leloo ung SS. Reul were wege y ol eg. Moel # rm MSE roo MSE l. Men Re. l. S Re. l. Segmeneem moel 5.67 * rron & Borer Prreol & Tom * Sne 8 rmeer,,,,,, n re re y e omonen of er, mernle volume n mernle weg, n mulneou emon e numer of rmeer for oe oun 8/.667 n e omonen n e yem. So for e weg euon, e ol numer of rmeer,, n r R j. R 6
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