Forest Mensuration IIForest Mensuration II

Lecture 11: Lecture 11: Stocking and Stand Stocking and Stand DensityDensity

Nick Buda Nick Buda Northwest Science and InformationNorthwest Science and InformationOntario Ministry of Natural ResourcesOntario Ministry of Natural Resources

November 16th, 2005November 16th, 2005Lakehead UniversityLakehead University

Reference: Avery, T.E. and H.E. Burkhart. 2002. Reference: Avery, T.E. and H.E. Burkhart. 2002. Forest Measurements 5th Ed. Chapter 15, pp. 321-Forest Measurements 5th Ed. Chapter 15, pp. 321-336.336.

Context

• “The stocking in this stand is too low.”

• “Plant this area to jack pine at 1700 stems/hectare”

• “Mark this stand to remove about 15 m2/ha of hard maple”

• “This stand is fully stocked”• “This stand is understocked”• “This stand is overstocked”

Context

Definitions

Density

Stocking

Summary

Definitions

Density:

• A quantitative term describing the degree of stem crowding within a stocked area*

• Can be expressed in absolute or relative terms

• Simply put: a measure of the amount of tree vegetation on a unit of land area

• Examples: 1700 stems/ha or 35 m2/ha, more…

Context

Definitions

•Density

•Stocking

Density

Stocking

Summary

Definitions

Stocking:

• Refers to the adequacy of a given stand density to meet some management objective*– Understocked, fully stocked, overstocked

• A stand considered “overstocked” for one management objective could be “understocked” for another

• Important to decide what constitutes full stocking - makes the use of this term confusing

• “Stocking” and “density” are often applied interchangeably - they are NOT the same thing

Context

Definitions

•Density

•Stocking

Density

Stocking

Summary

DensityDensity Relationships (for given species, site and

time period)

As Density Increases,

• Spacing• Average stem diameter• Crown Width• Live Crown Ratio• GTV per tree• MV per tree

Decrease

Context

Definitions

Density

•Relationships

•Measures

•Stems/unit area

•Basal Area

•SDI & 3/2 Law

•Relative Spacing

•CCF

•Point Density

Stocking

Summary

Increase

•Gross Total Volume per hectare•Merchantable Volume per hectare

After White (2004)

Density

Measures:

• Stems per unit area

• Basal Area

• Volume

• Various Indices

• Absolute vs. Relative Measures

Context

Definitions

Density

•Relationships

•Measures

•Stems/unit area

•Basal Area

•SDI & 3/2 Law

•Relative Spacing

•CCF

•Point Density

Stocking

Summary

Stand DensityStems per unit area:• Very useful in developing silvicultural

prescriptions• Variable density yield tables

e.g. 1700 stems per hectare, 2500 sph, 500 stems/ha, etc.

Context

Definitions

Density

•Relationships

•Measures

•Stems/unit area

•Basal Area

•SDI & 3/2 Law

•Relative Spacing

•CCF

•Point Density

Stocking

Summary

Black Spruce

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 20 40 60 80 100 120

Stand Age (years)

Stand Density (stems/ha)

Stand Density

Basal Area• A good, objective expression of density - very

commonly used - e.g. point sampling

Context

Definitions

Density

•Relationships

•Measures

•Stems/unit area

•Basal Area

•SDI & 3/2 Law

•Relative Spacing

•CCF

•Point Density

Stocking

Summary

Black Spruce

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120

Stand Age (years)

Stand Basal Area (m2/ha)

Stand DensityStand Density Index• A measure of density

based on 2 parts of BA - density and diameter of average tree

• Has been used in variable-density yield tables

• BA simpler and easier to use

3/2 Law of Self Thinning

• Foundation of Stand Density Management Diagrams (DMDs)

Context

Definitions

Density

•Relationships

•Measures

•Stems/unit area

•Basal Area

•SDI & 3/2 Law

•Relative Spacing

•CCF

•Point Density

Stocking

Summary

€

logV = −3/2logN + a

Stand Density

Relative Spacing

• Average distance between trees divided by the average height of the dominant canopy

• Main uses - mortality models & thinning schedules

• Tendency to decrease with age

Context

Definitions

Density

•Relationships

•Measures

•Stems/unit area

•Basal Area

•SDI & 3/2 Law

•Relative Spacing

•CCF

•Point Density

Stocking

Summary

€

RS =10000 /N

Hd

Stand DensityContext

Definitions

Density

•Relationships

•Measures

•Stems/unit area

•Basal Area

•SDI & 3/2 Law

•Relative Spacing

•CCF

•Point Density

Stocking

Summary

Crown Competition Factor• Reflects area available to average tree in a subject

stand, relative to maximum area it would use if open-grown

Establish crown width-dbh relationship

Compute maximum crown area (%ha)

Sum MCA values for each dbh class and divide by stand area

€

CW = b0 + b1(dbh)

€

MCA = πCW

2

⎛

⎝ ⎜

⎞

⎠ ⎟2

€

CCF =

MCAii=1

N

∑area

×100%

Point DensityContext

Definitions

Density

•Relationships

•Measures

•Stems/unit area

•Basal Area

•SDI & 3/2 Law

•Relative Spacing

•CCF

•Point Density

Stocking

Summary

• Stand density measures give an idea of the average density or competition for the whole stand

• Point density measures provide a competition index for a specific tree or point within a stand

• 3 main types:– Area-overlap - competion influence zone around tree - competition

stress a result of overlaps in zone

– Distance-weighted size ratio - idea that large trees close to subject tree exert more stress than small trees far away

– Polygon (area-available)€

CIi =1

Aia j

j=1

n

∑

€

CIi =D j /DiDISTijj=1

n

∑

Stocking

Recall:• stocking refers to the adequacy of a

given density to meet some management objective

Problem:• What should constitute full stocking for

a given species on a given site for a given management objective?

Fully-stocked or “normal stand”:• Hypothetically, a stand in which tree

crowns are fitted together so that no sunlight is wasted and each crown is matched with a root system that fully utilizes the soil

Context

Definitions

Density

Stocking

•Full Stocking

•Normality

•Regeneration

•Mature Stands

•Stocking Guides

Summary

Stocking

Regenerating Stands

• Stocking thought of as a measure of site occupancy

• i.e. The proportion of available areas occupied by tree seedlings (so as to result in a fully-stocked stand at maturity)

• Available area = growing space for one tree

Context

Definitions

Density

Stocking

•Full Stocking

•Normality

•Regeneration

•Mature Stands

•Stocking Guides

Summary

Stocking

Regenerating Stands• A percentage based stocking figure

does not tell you much about the distribution of the trees in a stand:

Context

Definitions

Density

Stocking

•Full Stocking

•Normality

•Regeneration

•Mature Stands

•Stocking Guides

Summary

2000 trees/ha 0 trees/ha

Clumped - 50% stocked

1000 trees/ha

Uniform - 50% stocked

Stocking

Mature Stands

• Essentially comparing the density of a subject stand to that of an “ideal” or reference stand– Volume– Basal Area

– An Example

Context

Definitions

Density

Stocking

•Full Stocking

•Normality

•Regeneration

•Mature Stands

•Stocking Guides

Summary

Stocking GuidesContext

Definitions

Density

Stocking

•Full Stocking

•Normality

•Regeneration

•Mature Stands

•Stocking Guides

Summary

Context

Definitions

Density

Stocking

•Full Stocking

•Normality

•Regeneration

•Mature Stands

•Stocking Guides

Summary

In a nutshell:

“…density tells what is, and stocking tells how this density relates to someone’s notion of what ought to be, usually in terms of percentages”

Smith et al. (1997)