The Model > Juvenile Growth > White Spruce

White Spruce

Height and diameter growth for juvenile white spruce (DBH<4 cm)

For juvenile white spruce, growth relationships are also based on an analysis in 2004 of combined data sets. These included Alberta LFS SDS data updated to May 2004, WESBOGY LTS data updated to Dec 2000, and regenerated permanent sample plot (rPSP) data contributed by Alberta forestry companies updated to Dec 2002.

Height Increment

The early white spruce height increment is similar to deciduous except the increment of small trees appears to decline to zero.

For juvenile white spruce (DBH<4cm) the annual height increment (HiSw, m/year) is represented by

HiSw = a [SFDec b][1 - exp(-H/d)]

Where: a = 1.15 SIHi6m / {[2b][1 - exp(- 6 / d]}

SFDec= 1/[Dec10H*(DecDen/10000)0.5], with a maximum value of 2; and if DecDen = 0 then SFDec = 2;

SFDec is spacing factor for juvenile deciduous trees (in tree lengths; unitless)

Dec10H is average height of tallest 10% the deciduous trees (m)

DecDen is deciduous tree density (stems/ha)

SIHi6m is the height increment given by the white spruce site index curve at 6m

H is the height of the tree at the start of the year (m),

b =0.0461, and d =1.5212

Applies to 1997 Site Index Curves:  When 1997 site index equations are selected a  1.15 dominance switching correction for the increment of juvenile spruce is applied. Feng et al. (2006 For Chron 82:819-824) determined that, under the Huang 1997 stem-analysis based site index curves, height increment was underestimated 15% for juvenile spruce. 

Applies to AESRD 2009 Site Index Curves: No dominant switching correction is applied

Note: that the parameter a is conditioned so that the juvenile height growth increment is 15% greater than the site index at the time the mature growth function takes over (aspen reach 4cm DBH at about 6m height). Due to dominant trees switching status as the thickest DBH tree during the early phase of stand development, the site trees used to estimate site index are generally shorter than the true height of the thickest tree in the juvenile phase. Magnussen and Penner (1996) developed a correction to recover early stand height for this switching. A recent application of this correction to boreal white spruce (Feng et al., 2006) indicated a 15% underestimate of height growth increment for juvenile white spruce.

Diameter Increment

There are 3 possible cases with respect to juvenile spruce annual diameter increment predictions:

Case 1: the tree began with a height below 1.3 m and after the current annual height increment continues to be below 1.3 m.

DBH is set to zero

Case 2: the tree began with a height below 1.3 m and after the current annual height increment, has crossed the 1.3 m height threshold. DBH is predicted as:

DBH = -2.22 + 1.988 * Ht

Where: Ht is the predicted height at the end of the growth year.

Case 3: the tree began with a height above 1.3. In this case DBH increment is obtained from an annual basal area increment (BAI, cm2/year) model

BAI = a*DBH*viewfactorb

Where: Viewfactor = arctan(1/sqrt(DecDenAbove/10000)*DH)/( p/2)
             DH = Dec10H-0.4*HT; of DH < 0.1 then DH = 0.1
              Viewfactor is constrained to <= 0.25 

Dec10H is the average height of the tallest 10% of all deciduous trees (m)

a = 1.609776, b = 0.208911


For juvenile white spruce, annual survival probability (Ps) is predicted using a logistic model.

Ps = exp(c) / (1+exp(c))

Where: c = d + e ln(H) + g (SwBagt)

H is tree height (m)

SwBagt is the basal area in thicker spruce (m2/ha)

d =5.546121, e =0.647729, g =-0.079591.