Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce

Abstract We derive and analyze a model that relates the growth rate of cross-sectional area (‘csa’) at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of c...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Valentine, Harry T. [verfasserIn] Mäkelä, Annikki [verfasserIn] Green, Edwin J. [verfasserIn] Amateis, Ralph L. [verfasserIn] Mäkinen, Harri [verfasserIn] Ducey, Mark J. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2011

Schlagwörter:	Allometry Growth model Pipe model Scaling Stem form

Übergeordnetes Werk:	Enthalten in: Trees - Berlin : Springer, 1986, 26(2011), 2 vom: 06. Sept., Seite 469-478
Übergeordnetes Werk:	volume:26 ; year:2011 ; number:2 ; day:06 ; month:09 ; pages:469-478

Links:	Volltext

DOI / URN:	10.1007/s00468-011-0608-0

Katalog-ID:	SPR006382339

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520			\|a Abstract We derive and analyze a model that relates the growth rate of cross-sectional area (‘csa’) at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to active csa within the crown. We also assume that the deactivation rate of csa beneath the crown is determined, in part, by the rate of crown rise. Integration of the growth-rate model under an additional assumption—that total crown length is constant after stand closure—provides a simple model of annual or periodic growth of total csa that can be fit to standard growth data. Three implications of the assumptions and integration are notable: (1) total csa within the crown scales allometrically with stem length above the cross section; (2) for a special case, total csa beneath the crown scales with stem length above the cross section; more generally, csa scales with a linear combination of the stem and crown lengths; and (3) the stem beneath the crown forms to approximate a frustum of a quadratic paraboloid. Basal area data from a loblolly pine (Pinus taeda L.) spacing trial show good agreement with (1) and (2), and with an empirical model developed from the special case of (2). Data from the plots of a Norway spruce (Picea abies (L.) Karst.) thinning trial, where crown length remained approximately constant, show good agreement with (2) and the empirical model. Prediction (3) is demonstrated by simulation.
650		4	\|a Allometry \|7 (dpeaa)DE-He213
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650		4	\|a Pipe model \|7 (dpeaa)DE-He213
650		4	\|a Scaling \|7 (dpeaa)DE-He213
650		4	\|a Stem form \|7 (dpeaa)DE-He213
700	1		\|a Mäkelä, Annikki \|e verfasserin \|4 aut
700	1		\|a Green, Edwin J. \|e verfasserin \|4 aut
700	1		\|a Amateis, Ralph L. \|e verfasserin \|4 aut
700	1		\|a Mäkinen, Harri \|e verfasserin \|4 aut
700	1		\|a Ducey, Mark J. \|e verfasserin \|4 aut
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952			\|d 26 \|j 2011 \|e 2 \|b 06 \|c 09 \|h 469-478

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author_variant	h t v ht htv a m am e j g ej ejg r l a rl rla h m hm m j d mj mjd
matchkey_str	article:14322285:2011----::oeseaigtmrwhorwlntdnmcapiainool
hierarchy_sort_str	2011
bklnumber	48.00
publishDate	2011
allfields	10.1007/s00468-011-0608-0 doi (DE-627)SPR006382339 (SPR)s00468-011-0608-0-e DE-627 ger DE-627 rakwb eng 580 630 640 ASE 48.00 bkl Valentine, Harry T. verfasserin aut Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We derive and analyze a model that relates the growth rate of cross-sectional area (‘csa’) at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to active csa within the crown. We also assume that the deactivation rate of csa beneath the crown is determined, in part, by the rate of crown rise. Integration of the growth-rate model under an additional assumption—that total crown length is constant after stand closure—provides a simple model of annual or periodic growth of total csa that can be fit to standard growth data. Three implications of the assumptions and integration are notable: (1) total csa within the crown scales allometrically with stem length above the cross section; (2) for a special case, total csa beneath the crown scales with stem length above the cross section; more generally, csa scales with a linear combination of the stem and crown lengths; and (3) the stem beneath the crown forms to approximate a frustum of a quadratic paraboloid. Basal area data from a loblolly pine (Pinus taeda L.) spacing trial show good agreement with (1) and (2), and with an empirical model developed from the special case of (2). Data from the plots of a Norway spruce (Picea abies (L.) Karst.) thinning trial, where crown length remained approximately constant, show good agreement with (2) and the empirical model. Prediction (3) is demonstrated by simulation. Allometry (dpeaa)DE-He213 Growth model (dpeaa)DE-He213 Pipe model (dpeaa)DE-He213 Scaling (dpeaa)DE-He213 Stem form (dpeaa)DE-He213 Mäkelä, Annikki verfasserin aut Green, Edwin J. verfasserin aut Amateis, Ralph L. verfasserin aut Mäkinen, Harri verfasserin aut Ducey, Mark J. verfasserin aut Enthalten in Trees Berlin : Springer, 1986 26(2011), 2 vom: 06. Sept., Seite 469-478 (DE-627)265505755 (DE-600)1463920-8 1432-2285 nnns volume:26 year:2011 number:2 day:06 month:09 pages:469-478 https://dx.doi.org/10.1007/s00468-011-0608-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-FOR SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 48.00 ASE AR 26 2011 2 06 09 469-478
spelling	10.1007/s00468-011-0608-0 doi (DE-627)SPR006382339 (SPR)s00468-011-0608-0-e DE-627 ger DE-627 rakwb eng 580 630 640 ASE 48.00 bkl Valentine, Harry T. verfasserin aut Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We derive and analyze a model that relates the growth rate of cross-sectional area (‘csa’) at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to active csa within the crown. We also assume that the deactivation rate of csa beneath the crown is determined, in part, by the rate of crown rise. Integration of the growth-rate model under an additional assumption—that total crown length is constant after stand closure—provides a simple model of annual or periodic growth of total csa that can be fit to standard growth data. Three implications of the assumptions and integration are notable: (1) total csa within the crown scales allometrically with stem length above the cross section; (2) for a special case, total csa beneath the crown scales with stem length above the cross section; more generally, csa scales with a linear combination of the stem and crown lengths; and (3) the stem beneath the crown forms to approximate a frustum of a quadratic paraboloid. Basal area data from a loblolly pine (Pinus taeda L.) spacing trial show good agreement with (1) and (2), and with an empirical model developed from the special case of (2). Data from the plots of a Norway spruce (Picea abies (L.) Karst.) thinning trial, where crown length remained approximately constant, show good agreement with (2) and the empirical model. Prediction (3) is demonstrated by simulation. Allometry (dpeaa)DE-He213 Growth model (dpeaa)DE-He213 Pipe model (dpeaa)DE-He213 Scaling (dpeaa)DE-He213 Stem form (dpeaa)DE-He213 Mäkelä, Annikki verfasserin aut Green, Edwin J. verfasserin aut Amateis, Ralph L. verfasserin aut Mäkinen, Harri verfasserin aut Ducey, Mark J. verfasserin aut Enthalten in Trees Berlin : Springer, 1986 26(2011), 2 vom: 06. Sept., Seite 469-478 (DE-627)265505755 (DE-600)1463920-8 1432-2285 nnns volume:26 year:2011 number:2 day:06 month:09 pages:469-478 https://dx.doi.org/10.1007/s00468-011-0608-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-FOR SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 48.00 ASE AR 26 2011 2 06 09 469-478
allfields_unstemmed	10.1007/s00468-011-0608-0 doi (DE-627)SPR006382339 (SPR)s00468-011-0608-0-e DE-627 ger DE-627 rakwb eng 580 630 640 ASE 48.00 bkl Valentine, Harry T. verfasserin aut Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We derive and analyze a model that relates the growth rate of cross-sectional area (‘csa’) at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to active csa within the crown. We also assume that the deactivation rate of csa beneath the crown is determined, in part, by the rate of crown rise. Integration of the growth-rate model under an additional assumption—that total crown length is constant after stand closure—provides a simple model of annual or periodic growth of total csa that can be fit to standard growth data. Three implications of the assumptions and integration are notable: (1) total csa within the crown scales allometrically with stem length above the cross section; (2) for a special case, total csa beneath the crown scales with stem length above the cross section; more generally, csa scales with a linear combination of the stem and crown lengths; and (3) the stem beneath the crown forms to approximate a frustum of a quadratic paraboloid. Basal area data from a loblolly pine (Pinus taeda L.) spacing trial show good agreement with (1) and (2), and with an empirical model developed from the special case of (2). Data from the plots of a Norway spruce (Picea abies (L.) Karst.) thinning trial, where crown length remained approximately constant, show good agreement with (2) and the empirical model. Prediction (3) is demonstrated by simulation. Allometry (dpeaa)DE-He213 Growth model (dpeaa)DE-He213 Pipe model (dpeaa)DE-He213 Scaling (dpeaa)DE-He213 Stem form (dpeaa)DE-He213 Mäkelä, Annikki verfasserin aut Green, Edwin J. verfasserin aut Amateis, Ralph L. verfasserin aut Mäkinen, Harri verfasserin aut Ducey, Mark J. verfasserin aut Enthalten in Trees Berlin : Springer, 1986 26(2011), 2 vom: 06. Sept., Seite 469-478 (DE-627)265505755 (DE-600)1463920-8 1432-2285 nnns volume:26 year:2011 number:2 day:06 month:09 pages:469-478 https://dx.doi.org/10.1007/s00468-011-0608-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-FOR SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 48.00 ASE AR 26 2011 2 06 09 469-478
allfieldsGer	10.1007/s00468-011-0608-0 doi (DE-627)SPR006382339 (SPR)s00468-011-0608-0-e DE-627 ger DE-627 rakwb eng 580 630 640 ASE 48.00 bkl Valentine, Harry T. verfasserin aut Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We derive and analyze a model that relates the growth rate of cross-sectional area (‘csa’) at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to active csa within the crown. We also assume that the deactivation rate of csa beneath the crown is determined, in part, by the rate of crown rise. Integration of the growth-rate model under an additional assumption—that total crown length is constant after stand closure—provides a simple model of annual or periodic growth of total csa that can be fit to standard growth data. Three implications of the assumptions and integration are notable: (1) total csa within the crown scales allometrically with stem length above the cross section; (2) for a special case, total csa beneath the crown scales with stem length above the cross section; more generally, csa scales with a linear combination of the stem and crown lengths; and (3) the stem beneath the crown forms to approximate a frustum of a quadratic paraboloid. Basal area data from a loblolly pine (Pinus taeda L.) spacing trial show good agreement with (1) and (2), and with an empirical model developed from the special case of (2). Data from the plots of a Norway spruce (Picea abies (L.) Karst.) thinning trial, where crown length remained approximately constant, show good agreement with (2) and the empirical model. Prediction (3) is demonstrated by simulation. Allometry (dpeaa)DE-He213 Growth model (dpeaa)DE-He213 Pipe model (dpeaa)DE-He213 Scaling (dpeaa)DE-He213 Stem form (dpeaa)DE-He213 Mäkelä, Annikki verfasserin aut Green, Edwin J. verfasserin aut Amateis, Ralph L. verfasserin aut Mäkinen, Harri verfasserin aut Ducey, Mark J. verfasserin aut Enthalten in Trees Berlin : Springer, 1986 26(2011), 2 vom: 06. Sept., Seite 469-478 (DE-627)265505755 (DE-600)1463920-8 1432-2285 nnns volume:26 year:2011 number:2 day:06 month:09 pages:469-478 https://dx.doi.org/10.1007/s00468-011-0608-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-FOR SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 48.00 ASE AR 26 2011 2 06 09 469-478
allfieldsSound	10.1007/s00468-011-0608-0 doi (DE-627)SPR006382339 (SPR)s00468-011-0608-0-e DE-627 ger DE-627 rakwb eng 580 630 640 ASE 48.00 bkl Valentine, Harry T. verfasserin aut Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We derive and analyze a model that relates the growth rate of cross-sectional area (‘csa’) at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to active csa within the crown. We also assume that the deactivation rate of csa beneath the crown is determined, in part, by the rate of crown rise. Integration of the growth-rate model under an additional assumption—that total crown length is constant after stand closure—provides a simple model of annual or periodic growth of total csa that can be fit to standard growth data. Three implications of the assumptions and integration are notable: (1) total csa within the crown scales allometrically with stem length above the cross section; (2) for a special case, total csa beneath the crown scales with stem length above the cross section; more generally, csa scales with a linear combination of the stem and crown lengths; and (3) the stem beneath the crown forms to approximate a frustum of a quadratic paraboloid. Basal area data from a loblolly pine (Pinus taeda L.) spacing trial show good agreement with (1) and (2), and with an empirical model developed from the special case of (2). Data from the plots of a Norway spruce (Picea abies (L.) Karst.) thinning trial, where crown length remained approximately constant, show good agreement with (2) and the empirical model. Prediction (3) is demonstrated by simulation. Allometry (dpeaa)DE-He213 Growth model (dpeaa)DE-He213 Pipe model (dpeaa)DE-He213 Scaling (dpeaa)DE-He213 Stem form (dpeaa)DE-He213 Mäkelä, Annikki verfasserin aut Green, Edwin J. verfasserin aut Amateis, Ralph L. verfasserin aut Mäkinen, Harri verfasserin aut Ducey, Mark J. verfasserin aut Enthalten in Trees Berlin : Springer, 1986 26(2011), 2 vom: 06. Sept., Seite 469-478 (DE-627)265505755 (DE-600)1463920-8 1432-2285 nnns volume:26 year:2011 number:2 day:06 month:09 pages:469-478 https://dx.doi.org/10.1007/s00468-011-0608-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-FOR SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 48.00 ASE AR 26 2011 2 06 09 469-478
language	English
source	Enthalten in Trees 26(2011), 2 vom: 06. Sept., Seite 469-478 volume:26 year:2011 number:2 day:06 month:09 pages:469-478
sourceStr	Enthalten in Trees 26(2011), 2 vom: 06. Sept., Seite 469-478 volume:26 year:2011 number:2 day:06 month:09 pages:469-478
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Allometry Growth model Pipe model Scaling Stem form
dewey-raw	580
isfreeaccess_bool	false
container_title	Trees
authorswithroles_txt_mv	Valentine, Harry T. @@aut@@ Mäkelä, Annikki @@aut@@ Green, Edwin J. @@aut@@ Amateis, Ralph L. @@aut@@ Mäkinen, Harri @@aut@@ Ducey, Mark J. @@aut@@
publishDateDaySort_date	2011-09-06T00:00:00Z
hierarchy_top_id	265505755
dewey-sort	3580
id	SPR006382339
language_de	englisch
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author	Valentine, Harry T.
spellingShingle	Valentine, Harry T. ddc 580 bkl 48.00 misc Allometry misc Growth model misc Pipe model misc Scaling misc Stem form Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce
authorStr	Valentine, Harry T.
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topic_title	580 630 640 ASE 48.00 bkl Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce Allometry (dpeaa)DE-He213 Growth model (dpeaa)DE-He213 Pipe model (dpeaa)DE-He213 Scaling (dpeaa)DE-He213 Stem form (dpeaa)DE-He213
topic	ddc 580 bkl 48.00 misc Allometry misc Growth model misc Pipe model misc Scaling misc Stem form
topic_unstemmed	ddc 580 bkl 48.00 misc Allometry misc Growth model misc Pipe model misc Scaling misc Stem form
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title	Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce
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title_full	Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce
author_sort	Valentine, Harry T.
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author_browse	Valentine, Harry T. Mäkelä, Annikki Green, Edwin J. Amateis, Ralph L. Mäkinen, Harri Ducey, Mark J.
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title_sort	models relating stem growth to crown length dynamics: application to loblolly pine and norway spruce
title_auth	Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce
abstract	Abstract We derive and analyze a model that relates the growth rate of cross-sectional area (‘csa’) at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to active csa within the crown. We also assume that the deactivation rate of csa beneath the crown is determined, in part, by the rate of crown rise. Integration of the growth-rate model under an additional assumption—that total crown length is constant after stand closure—provides a simple model of annual or periodic growth of total csa that can be fit to standard growth data. Three implications of the assumptions and integration are notable: (1) total csa within the crown scales allometrically with stem length above the cross section; (2) for a special case, total csa beneath the crown scales with stem length above the cross section; more generally, csa scales with a linear combination of the stem and crown lengths; and (3) the stem beneath the crown forms to approximate a frustum of a quadratic paraboloid. Basal area data from a loblolly pine (Pinus taeda L.) spacing trial show good agreement with (1) and (2), and with an empirical model developed from the special case of (2). Data from the plots of a Norway spruce (Picea abies (L.) Karst.) thinning trial, where crown length remained approximately constant, show good agreement with (2) and the empirical model. Prediction (3) is demonstrated by simulation.
abstractGer	Abstract We derive and analyze a model that relates the growth rate of cross-sectional area (‘csa’) at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to active csa within the crown. We also assume that the deactivation rate of csa beneath the crown is determined, in part, by the rate of crown rise. Integration of the growth-rate model under an additional assumption—that total crown length is constant after stand closure—provides a simple model of annual or periodic growth of total csa that can be fit to standard growth data. Three implications of the assumptions and integration are notable: (1) total csa within the crown scales allometrically with stem length above the cross section; (2) for a special case, total csa beneath the crown scales with stem length above the cross section; more generally, csa scales with a linear combination of the stem and crown lengths; and (3) the stem beneath the crown forms to approximate a frustum of a quadratic paraboloid. Basal area data from a loblolly pine (Pinus taeda L.) spacing trial show good agreement with (1) and (2), and with an empirical model developed from the special case of (2). Data from the plots of a Norway spruce (Picea abies (L.) Karst.) thinning trial, where crown length remained approximately constant, show good agreement with (2) and the empirical model. Prediction (3) is demonstrated by simulation.
abstract_unstemmed	Abstract We derive and analyze a model that relates the growth rate of cross-sectional area (‘csa’) at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to active csa within the crown. We also assume that the deactivation rate of csa beneath the crown is determined, in part, by the rate of crown rise. Integration of the growth-rate model under an additional assumption—that total crown length is constant after stand closure—provides a simple model of annual or periodic growth of total csa that can be fit to standard growth data. Three implications of the assumptions and integration are notable: (1) total csa within the crown scales allometrically with stem length above the cross section; (2) for a special case, total csa beneath the crown scales with stem length above the cross section; more generally, csa scales with a linear combination of the stem and crown lengths; and (3) the stem beneath the crown forms to approximate a frustum of a quadratic paraboloid. Basal area data from a loblolly pine (Pinus taeda L.) spacing trial show good agreement with (1) and (2), and with an empirical model developed from the special case of (2). Data from the plots of a Norway spruce (Picea abies (L.) Karst.) thinning trial, where crown length remained approximately constant, show good agreement with (2) and the empirical model. Prediction (3) is demonstrated by simulation.
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container_issue	2
title_short	Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce
url	https://dx.doi.org/10.1007/s00468-011-0608-0
remote_bool	true
author2	Mäkelä, Annikki Green, Edwin J. Amateis, Ralph L. Mäkinen, Harri Ducey, Mark J.
author2Str	Mäkelä, Annikki Green, Edwin J. Amateis, Ralph L. Mäkinen, Harri Ducey, Mark J.
ppnlink	265505755
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doi_str	10.1007/s00468-011-0608-0
up_date	2024-07-03T22:42:35.177Z
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Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce

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