Taper and stem outside-bark volume equations for five pine species in mixed-species forests in Mexico Gerónimo Quiñonez-Barraza1, Dehai Zhao2, Héctor M. De los Santos Posadas3 1Instituto
Nacional de Investigaciones Forestales Agrícolas y Pecuarias. km 4.5 Carretera Durango-Mezquital. Durango, Dgo. 34170, México. email:
[email protected] 2Warnell School of Forestry & Natural Resources, The University of Georgia, Athens, 180 E. Green St., Athens, GA 30602, USA. email:
[email protected] 3Colegio de Postgraduados, Campus Montecillo. km 36.5 Carretera México-Texcoco. Texcoco, Estado de México. 56230, México. email:
[email protected]
Introduction
Table 1: Taper and stem merchantable volume equations System
Taper and volume equations are basic components of stand inventory, growth and yield prediction, forest planning, and product simulation
CRS1 CRS2 CRS3
systems. Ten taper equations derived from upper-height based on
Variable-top equation 𝑉 ℎ = 𝛼0 𝐷 𝛼 1 𝐻 𝛼 2 1 − 1 − 𝑝
𝛼1
𝑉 ℎ = 𝛼0 𝐷 𝐻
𝛼2
1− 1−𝑝
𝑉 ℎ = 𝛼0 𝐷 𝛼 1 𝐻 𝛼 2 1 − 1 − 𝑝
Taper equation
𝛽1 𝛽2
𝑑 ℎ = 𝛼1 𝛼2 𝛽1 1−𝛽2 𝑒𝑥𝑝 −𝑒𝑥𝑝 𝛽3 𝐷 𝐻
taper-volume equation. These systems were simultaneously fitted to
taper and cumulative volume data for Arizona pine (Ap: Pinus arizonica Engelm.), Aztec pine (Azp: P. teocote Schiede ex Schltdl. & Cham.), Durango pine (Dp: P. durangensis Martínez), Mexican white pine (Mwp: P. ayacahuite Ehrenb. ex Schltdl.), and Smooth-leaves pine
𝛽1
CRS6 CRS7
𝑉 ℎ = 𝛼0 𝐷 𝛼 1 𝐻 𝛼 2 1 − 1 − 𝑝
𝑉 ℎ = 𝛼0 𝐷 𝛼 1 𝐻 𝛼 2 1 − 1 − 𝑝
𝛼1
CRS8
CRS9 CRS10
𝑉 ℎ = 𝛼0 𝐷 𝐻
𝛼2
1 + 𝛽1
𝛽1
𝐻−ℎ 𝐻𝛽3
𝑉 ℎ = 𝛼0 𝐷𝛼1 𝐻 𝛼2 − 𝛽2 𝐷 𝛽3 𝐻𝛽4 1 − 𝑝
CSS
𝑑 ℎ =
𝛼0 𝐷 𝛼1 𝐻 𝛼2 𝛽12 + 𝛽1 𝐻𝑘 𝛽1 + 𝑝 2
𝑑 ℎ =
𝛼0 𝐷 𝛼 1 𝐻 𝛼 2 − 𝛽1 𝛽2 𝑘
𝑑 ℎ =
𝛼0 𝐷 𝛼1 𝐻 𝛼2
𝑑 ℎ =
𝛽1 𝛽2 𝐷𝛽3 𝐻𝛽4 1 − 𝑝 𝑘𝐻
𝑐1 =
𝛼0 𝐷𝛼1 𝐻𝑖
𝛼2 −𝐾 Τ𝛽1
𝑑(ℎ) = 𝑐1
𝐻
𝛽1 −𝛽2 𝑒𝑥𝑝 −𝑒𝑥𝑝 𝛽3 𝐷𝛼1 𝐻 𝛼2
𝛽1 −1
1 − 𝛽1 𝑝
𝛽1 −1
𝛽1 + 𝛽2 1 − 𝑝
𝐻 − ℎ 𝛽2 −1 𝐻𝛽3
𝛽1 𝛽2 1−𝑝 𝑘𝐻
𝑘−𝛽1 Τ𝛽1
1− 1−𝑝
1−𝑝
𝛽2 −1
𝛽1 −1
𝑘−𝑅 Τ𝑅 𝐴 𝐼1 +𝐼2 1
𝐼
𝐴22
ൗ 𝛽1 𝑡0 − 𝑡1 + 𝛽2 𝑡1 − 𝐴1 𝑡2 + 𝛽3 𝐴1 𝑡2
𝑡0 = 1 − 𝑝0 𝐾Τ𝛽1 ; 𝑝0 = ℎ𝑏 Τ𝐻; 𝑡1 = 1 − 𝜗1 𝐾Τ𝛽1 ; 𝑡2 = 1 − 𝜗2 𝐾Τ𝛽2 1− 𝐼 +𝐼 𝐼 𝐼 𝐴1 = 1 − 𝜗1 𝛽2 −𝛽1 𝐾Τ𝛽1 𝛽2 ; 𝐴2 = 1 − 𝜗2 𝛽3 −𝛽2 𝐾Τ𝛽2 𝛽3 ; 𝑅 = 𝛽1 1 2 𝛽21 𝛽32 1 𝑠𝑖 𝜗1 ≤ 𝐻 ≤ 𝜗2 1 𝐼1 = ൝ ; 𝐼2 = ൝ 0 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 0 𝜗1 = ℎ1 Τ𝐻; 𝜗2 = ℎ2 Τ𝐻
𝑠𝑖 𝜗2
