Exercise 4 Allometric Equations
Problem: You need allometric relations established for a species for which you have no direct information, but the site index and fraction of light that penetrates through the canopy at ages 20, 70, and 150 years and yield tables that relate diameter to stem volume.
Solution: Use published volume tables to create allometric relations between stem diameter and tree mass, and determine appropriate relation between stem diameter and growth in foliage through simulations with 3-PG.
The LAI values were obtained using Beer’s Law and measured values of photosynthetically active radiation absorbed (fPAR) by a pure canopy of Douglas-fir, where
fPAR = 1-e –(k)(LAI); Example, If k = 0.5, LAI =6, then e-3.0 = 0.05 of PAR penetrates through canopy, fPAR = 1-0.05 = 0.95.
Use the following sequence of values and select the pair that best fit measured LAI and Stem Volume increment from Year 20-Year 160.
pFS2 pFS20 pFS2 pFS20
1.0 0.8 1.3 0.7
1.5 1.0 1.2 0.6
1.3 0.8 1.1 0.5
E. Record conventional form of allometric equation that predicts Foliage Mass, (kg)
as a function of stem diameter (b) in cm = (aF)*(bnF). Record derived parameters here:
Foliage Mass, kg =___________________.