Forest management recommendation based on q factor approach Introduction:

One of the main challenges with practicing uneven aged silviculture world wide is to regulate

its stocking and to maintain the stand structure in stable equilibrium. To manage the uneven

forest, different forest scientists and professionals had long been attempting to establish the

standard of check method for regulation of density in such stands.

The q factor approach is one of the most applied silvicultural guideline for regulating the

stocking of uneven aged forest world wide particularly in North America. The q factor is the

ratio of stem numbers in one size (DBH) class to the stem numbers in the next larger size

(DBH) class. It was first discovered by F. De Liocourt and since then was known as De

Liocourt’s law. However, many scientists including Meyer (1933)

Kerr (2001) and Cancino and Gadow (2002) have worked out equations or spreadsheet

calculation methods for this. As a partial work (10% of group assignment), this paper aims at

finding out the ideal stem per hectare (SPH) distribution by DBH classes for Coed Dolgarrog

slope assuming that the inventoried data represents the forest.

The standard equation for number of stem in any particular DBH class is given by:

10

ik diN k e− ⋅= ⋅ 1

Where,

k0,k1 are coefficients

di is mid-point of the diameter class

Ni is number of trees per diameter class;

and as defined above the q factor is given by:

1i

i

NqN

+= , where

Ni is the number of trees in one diameter class, and

Ni+1 is the number of trees in the next larger diameter class

1 All formulae copied and pasted from www.bangor.ac.uk/blackboard

Methods

This paper adopted the concept of ideal SPH distribution over size class calculation as

suggested by Kerr (2001) and Cancino and Gadow (2002). The consecutive steps are briefly

described for the sake of clear understanding:

Step one: Input Variables and assumptions

There are four input variables for calculation of the ideal distribution the DBH class width,

target basal area (m.sq/ha), target DBH (cm) and the q factor. As per the recommendation of

Kerr (2001), the target basal area, target DBH and q factor were assumed to be 30, 50 and

1.3. Similarly, since the DBH class width was 4 in the field inventory data analysis, it was

adhered with this calculation.

Step two: Calculation of Constant K3 by using 1 23

140000

ci

ii

k q dπ −

=

= ⋅ ⋅∑ 2, Where

c is the number of diameter classes 1iq − is the q-factor raised to the power i-1, this calculation assumes the uniform q = 1.3 for

diameter classes for simplicity, therefore, 1iq − =1.3

K3 is calculated to estimate the number of stem in largest (target) diameter class by dividing

the target basal area with k3 constant (described in next step)

Table 1: The calculation of Constant di i qi-1*di

2 di i qi-1*di2

5 12 448.040 33 5 3110.293

9 11 1116.654 37 4 3007.693

13 10 1792.160 41 3 2840.890

17 9 2357.462 45 2 2632.500

21 8 2767.210 49 1 2401.000

25 7 3016.756 53 0 0.000

29 6 3122.574 k3 2.247

Step three: Estimation of N1

The number of the number of stems in target diameter class is calculated by the formula,

13

BAN

k= target = 30/2.247= 13, therefore there should be 13 number of stem per hectare (SPH;

ref table 2; DBH Class 49).

Step four: Determination of ideal diameter distribution using assumed q factor and N1

2 (Calculated as Cancino and Gadow, 2002; Kerr’s formula for k3 differ from it which yields k3 = 2.58; Ref. q factor.xls)

The formula, 1i iN q N −= ⋅ was used to determine the SPH of i th DBH Class; For

example, the number of stem in DBH Class 45 = 1.3 * 13 = 17.

Result and Discussion:

Table 2 shows the result of inventory (real) and ideal distribution of stem per hectare (SPH).

Similarly, the figure 1 illustrates the visual comparison of real (zigzag curve) and ideal

distribution (reverse J shape curve) of SPH over diameter classes.

As evident from the difference (334) of sum of SPH real (632) and SPH ideal (966); the

forest stand is under stocked. The next interpretation of result is that there is crowding of

sapling in DBH class 5, which needs to be removed for competition reduction. Similarly, the

DBH class 29 and 37 shows slight increase over the ideal SPH which technically should be

thinned, however, considering the species (it is Oak), it is better to retain them as seed

bearers because of poor existing regeneration of Oak on the site.

Table 2: Real Inventory +Ideal (equilibrium) data at Dolgarrog Slope

DBH class

Frequency (4*15*15 m^2 Plots)

SPH (real)

BA real (sq.m/ha)

SPH (ideal)

BA ideal (sq.m/ha)

Difference in SPH

5 22 244 0.479 233 0.457 -11

9 9 100 0.636 179 1.140 79

13 8 89 1.181 138 1.830 49

17 1 11 0.25 106 2.407 95

21 1 11 0.381 82 2.825 71

25 3 33 1.62 63 3.080 30

29 5 56 3.699 48 3.188 -8

33 3 33 2.822 37 3.176 4

37 3 33 3.548 29 3.071 -4

41 1 11 1.452 22 2.901 11

45 0 0 0 17 2.688 17

49 1 11 2.074 13 2.451 2

53 0 0 0 0 0.000 0

Sum 632 966 334

Figure 1: Ideal and Real Distribution of Stem per ha in Dolgarrog Forest (Slope)

0

50

100

150

200

250

300

5 9 13 17 21 25 29 33 37 41 45 49 53

DBH classes

SPH Real

Ideal

Conclusion:

Application of q factor approach to regulate the stocking of uneven aged forest is becoming

wide spread and can be used in Coed Dolgarrog as a silvicultural guideline for stocking

management, control and monitoring. Besides using the SPH, equilibrium basal area

(calculated in the table) or equilibrium growing stock (multiplying form height on basal area)

can also be achieved through this approach.

References:

Cancino, J. and Gadow, K., 2002: Stem number guide curves for uneven-aged forests

development and limitations. In: Gadow, K., Nagel, J. and Saborowski, J. (Eds.), 2002:

Continuous Cover Forestry. Assessment, Analysis, Scenarios. Kluwer Academic

Publishers, Dordrecht, 163-174.

Kerr, G., 2001: An improved spreadsheet to calculate target diameter distributions in

uneven-aged silviculture. Continuous Cover Forestry Group Newsletter 19, 18-20.

www.bangor.ac.uk/blackboard; University of Bangor, Wales’s website, cited on

23/03/2008