Application of the pipe model theory to predict canopy leaf area

1982 ◽  
Vol 12 (3) ◽  
pp. 556-560 ◽  
Author(s):  
R. H. Waring ◽  
P. E. Schroeder ◽  
R. Oren
Keyword(s):  
Leaf Area ◽  
Model Theory ◽  
Large Fraction ◽  
Cross Sectional Area ◽  
Unit Weight ◽  
Sectional Area ◽  
Cross Sectional ◽  
Sapwood Area ◽  
Pipe Model ◽  
Pipe Model Theory

The pipe model theory presents the idea that a unit weight of tree foliage is serviced by a specific cross-sectional area of conducting sapwood in the crown. Below the crown, a large fraction of the tree bole may be nonconducting tissue, so the sapwood area would have to be known to estimate foliage. We applied the pipe model theory to the analysis of several western coniferous species to learn whether the distribution of canopy leaf area could be accurately estimated from knowledge of the sapwood cross-sectional area at various heights, including breast height (1.37 m). Results are excellent, but taper in the conducting area must be considered when sapwood area is measured below the crown.

The applicability of the pipe model theory for the prediction of foliage biomass in trees from natural, untreated black spruce stands

1992 ◽  
Vol 22 (8) ◽  
pp. 1118-1123 ◽  
Author(s):  
Edgar Robichaud ◽  
Ian R. Methven
Keyword(s):  
Model Theory ◽  
Black Spruce ◽  
Strong Relationship ◽  
Cross Sectional Area ◽  
Social Classes ◽  
Regression Equations ◽  
Sectional Area ◽  
Cross Sectional ◽  
Pipe Model ◽  
Pipe Model Theory

Trees were sampled from 26 black spruce (Piceamariana (Mill.) B.S.P.) stands across New Brunswick and within the boreal forest of Quebec to test the validity of the pipe model theory for sampling purposes. Trees were sampled from a wide range of ages, site qualities, densities, and social classes for determination of foliage biomass and sapwood cross-sectional areas at breast height and at the base of the live crown. A strong relationship was found between sapwood cross-sectional area and foliage biomass across the range of conditions. The y-intercepts for these regression equations, based on the untransformed data, were not significantly different from zero (P < 0.05). Partial correlation analysis indicated no significant relationship between the foliage biomass and tree age, site quality, or stand density but confirmed the strong relationship with sapwood cross-sectional area. Suppressed and intermediate social classes followed a similar relationship as dominant trees. Regression equations developed from this study were similar to those determined for spruce species and supported the use of sapwood cross-sectional area as a predictor of foliage biomass for black spruce.

Leaf area – sapwood cross-sectional area relationships in repressed stands of lodgepole pine

1987 ◽  
Vol 17 (3) ◽  
pp. 205-209 ◽  
Author(s):  
M. G. Keane ◽  
G. F. Weetman
Keyword(s):  
Hydraulic Conductivity ◽  
Leaf Area ◽  
Wood Density ◽  
Lodgepole Pine ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Density Profiles ◽  
Individual Tree ◽  
Individual Trees

To better understand the phenomenon of growth "stagnation" in high-density lodgepole pine (Pinuscontorta Dougl. ex Loud.), leaf area and its relationship with sapwood cross-sectional area were examined on both an individual tree and stand basis. Leaf areas of individual trees in a 22-year-old stand varied from 30.8 m2 (dominants in stands of low stocking) to 0.05 m2 (suppressed trees in stands of high stocking). Leaf area indices ranged from 13.4 to 2.3 m2 m−2 between low and high stocking levels, respectively. Over the same stocking range, the ratio of leaf area to sapwood cross-sectional area was reduced from 0.3 to 0.15 m2 cm−2. Intraring wood density profiles showed that ovendry density increased from 0.52 to 0.7 g cm−3 and the proportion of early wood decreased over a stocking level range of 6500–109 000 trees/ha. A reduction in hydraulic conductivity in the stems of stagnant trees, suggested by the greater proportion of narrow-diameter tracheids present, may lead to a greater resistance to water transport within the boles of trees from stagnant stands, leading to low leaf areas.

Estimating leaf area of Abieslasiocarpa across ranges of stand density and site quality

1989 ◽  
Vol 19 (7) ◽  
pp. 930-932 ◽  
Author(s):  
James N. Long ◽  
Frederick W. Smith
Keyword(s):  
Leaf Area ◽  
Species Differences ◽  
Stand Density ◽  
Cross Sectional Area ◽  
Site Quality ◽  
Sectional Area ◽  
Cross Sectional ◽  
Breast Height ◽  
Unbiased Estimates ◽  
Stand Conditions

For a given species, differences in the relation between leaf area and sapwood cross-sectional area at breast height have been attributed to the effects of varying stand density and site quality. When leaf area of Abieslasiocarpa (Hook.) Nutt. is estimated as a function of sapwood cross-sectional area at breast height and distance from breast height to the midpoint of the crown, the apparent effects of stand density and site quality are eliminated. A comparison of these results with those for Pinuscontorta Dougl. suggests this model form should provide unbiased estimates of leaf area for a variety of species and stand conditions.

scholarly journals RELATIONSHIPS OF LEAF AREA AND TRUNK DIAMETER OF APPLE TREES AFFECTED BY ROOTSTOCK AN D CULTIVAR

HortScience ◽  
1992 ◽  
Vol 27 (11) ◽  
pp. 1169c-1169
Author(s):  
Curt R. Rom ◽  
Renae E. Moran
Keyword(s):  
Leaf Area ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Mature Trees ◽  
Apple Trees ◽  
Cross Sectional ◽  
Trunk Diameter ◽  
Yield Efficiency ◽  
Linear Relationships ◽  
Old Trees

Trunk cross-sectional area (TCA) has been used to estimate leaf area (LA) and yield efficiency but variation in LA and TCA relationships have been unexplored. LA and TCA of 10-yr-old 'Starkspur Supreme Delicious' on 9 rootstocks (STKs) were measured in 1989. LA and TCA of 2-yr-old trees of 3 cultivars (CVs) on 5 STKs were measured in 1991. Regression of LA and TCA was performed for each CV, STK and each CV/STK. On mature trees, LA varied significantly with STK. The number and LA of shoot leaves (LVS) and spur LVS varied with STK but the % of total was not significantly different (approx. 52% spur LVS). The relationships of LA and TCA were linear for mature (r2=.94) and young (r2=.44) trees. On young trees, TCA varied with CV, but LA did not. Both LA and TCA were significantly different among STKs. The linear relationships of LA and TCA had unique intercepts with each CV, STK and CV/STK combination but slopes were not significantly different. Leaf area of Jonagold' and 'Gala' tended to increase more with increasing TCA than 'Empire'.

Influence of fertilization on the allometric relations for two pines in contrasting environments

1993 ◽  
Vol 23 (8) ◽  
pp. 1704-1711 ◽  
Author(s):  
Stith T. Gower ◽  
Brent E. Haynes ◽  
Karin S. Fassnacht ◽  
Steve W. Running ◽  
E. Raymond Hunt Jr.
Keyword(s):  
Leaf Area ◽  
Ponderosa Pine ◽  
Cross Sectional Area ◽  
Red Pine ◽  
Stem Diameter ◽  
Sectional Area ◽  
Cross Sectional ◽  
Breast Height ◽  
Allometric Relations ◽  
And Control

The objective of this study was to examine the effect of fertilization on the allometric relations for red pine (Pinusresinosa Ait.) and ponderosa pine (Pinusponderosa Dougl. ex Laws.) growing in contrasting climates. After 2 years of treatment, fertilization did not significantly affect the allometric relations between stem or branch mass and stem diameter for either species. For a similar-diameter tree, current foliage mass and area and new twig mass were significantly greater for fertilized than for control red pine and ponderosa pine. The significant increase in new foliage mass and area occurred in the upper and middle canopy for red pine and middle and lower canopy for ponderosa pine. For a similar-diameter tree, projected (one-sided) leaf area and total foliage mass were significantly greater for fertilized than for control red pine. However, leaf area and total foliage mass did not differ between similar-diameter fertilized and control ponderosa pine because fertilization decreased leaf longevity. The ratios of leaf area/sapwood cross-sectional area measured at breast height (1.37 m) were 0.14 and 0.11 for control plus fertilized red pine and ponderosa pine, respectively, and were greater (but not significantly) for fertilized than for control trees, while the ratios of leaf area/sapwood cross-sectional area measured at the base of live crown were significantly greater for fertilized than for control red pine and ponderosa pine.

Crown condition, needle mass, and sapwood area relationships of Norway spruce (Picea abies)

2000 ◽  
Vol 30 (10) ◽  
pp. 1646-1654 ◽  
Author(s):  
Otto Eckmüllner ◽  
Hubert Sterba
Keyword(s):  
Picea Abies ◽  
Norway Spruce ◽  
Condition Assessment ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Crown Condition ◽  
Cross Sectional ◽  
Sapwood Area ◽  
Good Estimator ◽  
Needle Mass

Crown-condition assessment, hypothesized to estimate needle losses following damage from several sources, one of which might be air pollution, suffers from the subjective notion of a standard "healthy" tree. On the other hand, the foliage biomass - sapwood area ratios are reported to depend on a number of factors, e.g., site quality, stand density, crown class, and tree ring width conductivity. The authors hypothesize that early sapwood area might help to even better estimate needle biomass of Norway spruce (Picea abies (L.) Karst.) and to help standardize crown-condition assessment. Thirty-six Norway spruce trees at two Austrian sites, from three age-classes, three crown classes, and two crown-condition classes were felled. Needle mass, cross-sectional area, sapwood area, and early sapwood area (i.e., sapwood area excluding latewood) were measured. The results of this study indicate that indeed early sapwood area is a good estimator of foliage, independent of site, age, crown class, and crown condition. The ratio between early sapwood area and cross-sectional area could be a good estimator for crown condition and thus help to standardize crown-condition assessments by different surveyors.

Foliage–sapwood area relationships for Abiesbalsamea in central Maine, U.S.A.

1996 ◽  
Vol 26 (12) ◽  
pp. 2071-2079 ◽  
Author(s):  
Daniel W. Gilmore ◽  
Robert S. Seymour ◽  
Douglas A. Maguire
Keyword(s):  
North America ◽  
Leaf Area ◽  
Linear Model ◽  
Geographical Region ◽  
Cross Sectional ◽  
Sapwood Area ◽  
Northeastern North America ◽  
Leaf Mass ◽  
Pipe Model ◽  
Log Linear

Studies of forest productivity commonly invoke the pipe-model theory, which implies that leaf area or leaf mass in the tree crown is proportional to cross-sectional xylem (sapwood) area below the crown, to estimate leaf area or leaf mass from cross-sectional sapwood area. Prior ecophysiological studies have suggested that models to predict projected leaf area (PLA) from sapwood area for Abiesbalsamea (L.) Mill, are valid across a broad geographical region in northeastern North America. However, no single study has explicitly tested the applicability of different model forms to predict PLA from sapwood area. The objectives of this study were to (1) test the consistency of leaf area/sapwood area ratios at the base of the live crown among four canopy positions, (2) select the best sapwood-based model out of several published model forms to predict projected leaf area, (3) explore the ability of nonsapwood-based models to predict projected leaf area, and (4) test the validity of a common model to predict projected leaf area for A. balsamea in central Maine, U.S.A. We detected no strong statistical differences in the leaf area/sapwood area ratio at the base of the live crown among the open-grown, codominant, intermediate, and suppressed canopy positions. Using a modified likelihood criterion to compare the ability of various model forms to predict PLA, we found that a log–linear model incorporating sapwood area at breast height (BH) and crown length (CL) performed the best, but a log–linear model with CL as the sole predictor variable also performed well. We concluded that a single logarithmically transformed model form using sapwood area at BH and CL to predict PLA is valid among canopy positions, but a single model to predict LA from sapwood area is not valid across a broad geographical region in northeastern North America.

scholarly journals Crown allometry and application of the pipe model theory to white spruce (Picea glauca (Moench) Voss) and aspen (Populus tremuloides Michx.) in the western boreal forest of Canada

2016 ◽  
Vol 46 (2) ◽  
pp. 262-273 ◽  
Author(s):  
Derek F. Sattler ◽  
Philip G. Comeau
Keyword(s):  
Boreal Forest ◽  
Populus Tremuloides ◽  
Model Theory ◽  
Picea Glauca ◽  
White Spruce ◽  
Allometric Relationship ◽  
Sapwood Area ◽  
Crown Length ◽  
Pipe Model ◽  
Pipe Model Theory

White spruce (Picea glauca (Moench) Voss) and aspen (Populus tremuloides Michx.) from unmanaged stands in the boreal forest of Alberta, Canada, were examined for two of the main structural assumptions in the process-based model CROBAS: (i) a constant allometric relationship between foliage mass and crown length and (ii) a constant relationship between foliage mass and sapwood area. We evaluated these relationships at both at the whole-crown and within-crown levels. Results indicated that for both species, a constant allometric relationship between foliage mass and crown length was maintained at the whole-crown level over a period exceeding the peak mean annual increment of each species. Within the crowns of spruce, foliage mass accumulated faster near the tree apex as total crown length increased. For aspen, the increase in foliage mass per unit crown length for any section within the crown showed greater similarity to the relationship observed at the whole-crown level. The assumption of a constant relationship between foliage mass and sapwood area at the crown base generally held for spruce but showed considerable variation for any given diameter class. For aspen, this assumption did not appear to be appropriate. For both species, there was more foliage mass per unit sapwood area with increasing height from the ground for nearly all tree size classes. This latter finding was in conflict with the pipe model theory but could not be explained by the hydraulic theory of crown architecture, which predicts a decrease in the ratio of foliage mass to sapwood area with increasing path length.

scholarly journals A Method for Quantifying Whole-tree Pruning Severity in Mature Tall Spindle Apple Plantings

HortScience ◽  
2017 ◽  
Vol 52 (9) ◽  
pp. 1233-1240 ◽  
Author(s):  
James R. Schupp ◽  
H. Edwin Winzeler ◽  
Thomas M. Kon ◽  
Richard P. Marini ◽  
Tara A. Baugher ◽  
...  
Keyword(s):  
Leaf Area ◽  
Fruit Size ◽  
Titratable Acidity ◽  
Severity Index ◽  
Cross Sectional Area ◽  
Soluble Solids ◽  
Sectional Area ◽  
Cross Sectional ◽  
The Cross ◽  
Whole Tree

Pruning is the cutting away of vegetation from plants for horticultural purposes. Pruning is known to reduce apple tree size, increase fruit size and quality, and decrease yield. Methods for studying the effects of varying degrees of severity of pruning on a whole-tree basis have used qualitative descriptions of treatments rather than repeatable whole-tree quantitative metrics. In this study, we introduce a pruning severity index calculated from the sum of the cross-sectional area of all branches on a tree at 2.5 cm from their union to the central leader divided by the cross-sectional area of its central leader at 30 cm from the graft union. This limb to trunk ratio (LTR) was then modified by successively removing the largest branches of ‘Buckeye Gala’ to achieve six severity levels ranging from LTR 0.5 to LTR 1.75, with lower values representing more extreme pruning with less whole-tree limb area relative to trunk area. Pruning treatments were applied for three consecutive years and tree growth and cropping responses were observed for the first 2 years. With increasing pruning severity the following characteristics increased after seasonal growth: number of renewal limbs, number of shoots, shoot length, number of shoot leaves, shoot leaf area, final fruit set, fruit size, yield of large fruit, crop value from large fruit, soluble solids, and titratable acidity. The following characteristics decreased: limb age, number of secondary limbs, number of spurs, number of spur leaves, spur leaf area, the ratio of spur leaf area to shoot leaf area, fruit count per tree, yield, yield efficiency, crop value from small fruit, overall crop value, and sugar:acid ratio. The LTR provides a measurable way to define and create different levels of pruning severity and achieve consistent outcomes. This allows a greater degree of accuracy and precision to dormant pruning of tall spindle apple trees. The use of the LTR to establish the level of pruning severity allows the orchard manager to set crop load potential through regulation of the canopy bearing surface. This metric is also a necessary step in the development of autonomous pruning systems.

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