Q Factor In Forest Management

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:

N i = k0 ⋅ e − k1 ⋅di 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: q =

N i + 1 , where N i

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 k3 =

π 40000

c

⋅ ∑ q i −1 ⋅ di2 2, Where i =1

c

is the number of diameter classes

q i −1

is the q-factor raised to the power i-1, this calculation assumes the uniform q = 1.3 for diameter classes for simplicity, therefore, q i −1 =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

qi-1*di2

i

di

qi-1*di2

i

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, N1 =

BAtarget k3

= 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, N

i

=

q ⋅ N

i − 1

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

Frequency DBH

(4*15*15 m^2

SPH

BA real

SPH

BA ideal

Difference

class

Plots)

(real)

(sq.m/ha)

(ideal)

(sq.m/ha)

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) 300 250

SPH

200 Real

150

Ideal

100 50 0 5

9

13

17

21

25

29

33

37

41

45

49

53

DBH classes

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