characterizing stand density for stand tending...

Characterizing Stand Density for

Stand Tending Strategies

ESRM 323

Chpt. 4

Smith, et al.

… or, What tools are available to help us quantify how much growing space the trees are using on this site …

… compared to the trees on this site:

Some Stand Attribute Definitions •  Trees per unit area (TPA) – Average number

of live trees existing on a characteristic unit of area. The most basic measure of stand density. (In U.S.A., units are Trees Per Acre.)

•  Diameter Breast Height (DBH) – average diameter of a tree stem (trunk, or bole) measured 4.5 feet above general ground level on flat or gently sloping terrain, otherwise measured from the uphill side on sloping terrain. (In U.S.A., units are inches.) 4

Some Stand Attribute Definitions …

•  Mean DBH (AveDBH) - The simple arithmetic mean DBH of all trees in the stand (inches).

•  Basal area (ba, sometimes g) – cross-sectional area of a tree stem at breast height, assuming circular cross-sectional shape. (In U.S.A., units are square feet.)

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Some Stand Attribute Definitions …

•  Quadratic Mean DBH (DBHq, QMD, or sometimes Dg) – the DBH of the tree with mean basal area

•  Stand Basal Area (SBA, TBA, BA, or G) – sum of individual tree basal areas in a stand §  BA = 0.005454 x QMD2 x TPA

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Some Stand Attribute Definitions …

•  DBH distribution –  The frequency (histogram) of tree diameters in a

stand. –  Characterized as the number of trees per acre in

one or two inch diameter classes –  Information from the stand’s diameter distribution

is often used to characterize the stand’s structure, to characterize within stand competition, and to target particular tree sizes in application of different thinning methods

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Some Stand Attribute Definitions … •  DBH distribution

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Some Stand Attribute Definitions … •  Height – (H, AveHt) Arithmetic mean height of

all trees in a stand (in U.S.A., ft.) •  Dominant Height – Average height of

dominant trees (may be average of dominant and codominant, there are other ways to define, also …)

•  Top Height – Average height of 100 largest diameter trees on a hectare (lgst. 40 / acre in U.S., sometimes denoted H40, units are feet)

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Stocking vs. Stand Density

•  STOCKING

–  A loose term for the amount of anything on a given area, particularly in relation to what is considered to be optimum.

–  In a forest, a more or less subjective indication of the number of trees as compared to the desirable number for "best" results.

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Stocking vs. Stand Density … •  STOCKING …

–  More precisely, a measure of the proportion of an area actually occupied by trees, expressed e.g., in terms of stocked quadrats or percent crown closure, as distinct from their stand density.

–  Adequacy of a given amount of material to meet some management objective. Accordingly, stands can be referred to as "understocked," "fully stocked," or "overstocked." A particular stand that is overstocked for one management objective could be "understocked" for another objective.

–  (Ford-Robertson 1977) 11

Stocking vs. Stand Density … •  STAND DENSITY

–  A quantitative measure of tree stocking expressed either relatively as a coefficient, taking normal numbers, basal area or volume as unity, or absolutely, in terms of number of trees per acre, total basal area, or volume, per unit area.

–  More precisely, a measure of the degree of crowding of trees within stocked areas, -- of crown length to tree height; crown diameter to DBH, or crown diameter to tree height; or of stem spacing to tree height.

–  (Ford Robertson 1977) 12

Some Stand Density Metrics

•  Simple indicators of stand density (absolute measures): – number per unit area (equivalent to "density" in

ecological usage) – basal area per unit area – crown closure usually expressed as % crown

cover (can be obtained easily from aerial photos)

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Some Stand Density Metrics …

•  Density indexes (relative measures comparing a given stand to a “standard”) – Usually involve two (2) stand attributes

•  Percent Normality, N% (McArdle, et al. 1930) •  Stand Density Index, SDI (Reineke 1933) •  Relative Density Index, RDI (Drew & Flewelling 1979) •  Relative Density, Curtis’ RD (Curtis 1982)

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Some Stand Density Metrics …

•  Percent Normality –  Based on Normal Yield, i.e., the yield that results when

the trees are fully occupying the site –  Knowing the age and site index for a particular stand,

its basal area can be expressed as a percentage of normal BA for same age and site:

N%= BAOBAN

100⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

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Some Stand Density Metrics … •  Percent Normality

Stand Density Index (SDI) (Reineke 1933)

•  Combines Trees Per Acre with average tree size, QMD

•  Based on a pre-determined limiting relationship between log(QMD) and log(TPA)

•  Expresses density of a stand in terms of an equivalent number of 10-inch trees

•  The higher the SDI, the more crowded the stand

ln(TPA)=ln(a)−1.605⋅ln(QMD)

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Stand Density Index (SDI)

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Log

TPA

log QMD

Maximum

obs

log 10

SDI

Stand Density Index (SDI) …

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Stand Density Index (SDI) … •  Shortcut formula:

•  SDI increases with either an increase in number of stems per acre or an increase in QMD, or both

•  The higher the SDI, the more crowded the stand •  Relative SDI,

SDI =TPA QMD10

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

1.605

SDIREL= SDISDIMAX

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

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Stand Density Index (SDI) …

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Relative Density Index (RDI) (Drew & Flewelling 1979)

• Combines number per acre with average tree size, volume (cu.ft)

• Based on the – 3/2 power “law” of self-thinning

- For Douglas-fir in PNW, ln(a)=12.644

v=aTPA−3/2 or ln(v)= ln(a)−3/2⋅ln(TPA)

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Relative Density Index (RDI) (Drew & Flewelling 1979)

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ln v

ln TPA

Normal

Maximum

obs

ln TPAmax ln TPAo

Relative Density Index (RDI)

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ln vo

Relative Density Index (RDI)

• Relative Density Index,

• Relative Density Index is usually interpreted as the proportion of the total growing space being utilized by trees

ρr=TPAobsTPAmax

TPAmax=e

12.644−ln(v)1.5

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

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The Density Management

Diagram (DMD)

A B C

D - Lower limit of acceptable total yield (per ac.)

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Basic Tenets for using the DMD

• Stands growing below the crown closure line (RDI = 0.15; RD ~ 15), are not fully utilizing the site, and density could be increased without decreasing mean tree growth.

• Maximum tree size can be obtained most quickly by managing stands near the crown closure line.

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Basic Tenets for using the DMD …

•  Stands managed near the lower bound of the zone of imminent competition-mortality down to a Relative Density Index of about 0.35 to 0.40 (RD ~ 35 to 40) will have somewhat greater total stand growth than stands managed at lesser densities, but will have smaller individual tree sizes

•  Stands should not be allowed to enter the zone of imminent competition-mortality (RDI = 0.55; RD ~ 55) until several years before the final harvest in order to avoid a severe reduction in vigor and potential damage to the crop trees.

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Relative Density (RD) (Curtis 1982)

•  Combines stand basal area and average tree size, ie., QMD (or, DBHq)

•  RD = BA / (QMD)0.5

•  RD will increase with an increase in BA (with constant QMD)

•  RD will increase with a decrease in QMD for constant BA

•  Thus, higher values of RD imply a greater degree of competition

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Standard %Normality

(BA)

RDI

(Flewelling)

RD

(Curtis)

Maximum 150 1.0 100

Normal 100 0.67 70

Upper thinning

limit

75-80 0.5 50

Lower thinning

limit

50 - 60 0.3 35

Crown closure 30 0.15 20

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Approximate relationship between selected stand density measures

Uses of Density Indexes •  They are useful descriptors of stand conditions

(though not a complete description) •  They are useful predictors of growth (in

combination with other variables) •  They serve as guides to thinning and stand

treatment, defining the following – –  Maximum size-density limit (“A” line) –  Upper thinning limit, above which one expects

substantial mortality and/or unacceptable diameter growth (“B” line)

–  Point of crown closure in young stands (“C” line) –  Lower thinning limit, below which one expects

unacceptable total volume growth (“D” line) 31

Uses of Density Indexes …

•  They can also be used to estimate desirable planting numbers and desirable number of residual trees in pre-commercial thinning (e.g., RD).

•  Can be used to translate multiple objectives into actionable metrics, ie., metrics that can be used to take action, eg., habitat requirements

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Stand Development

Stages

Impacts Wildlife Populations

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Stem Exclusion Understory Re-iniit. Stand Initiation Old Growth

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Using the DMD for Wildlife Habitat

UH - Upper limit for appreciable Wildlife Habitat (CurtisRD = 45; RDI ~ 0.45) LH - Lower limit for appreciable Wildlife Habitat (CurtisRD = 25; RDI ~ 0.25)

Summary Ideas

•  As stand dynamics progress, the growing space is reallocated to different trees mostly as a result of competition

•  Manipulating growing space is the major tool available to the silviculturist to accelerate (decelerate) the approach to desired (undesired) stand outcomes

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Summary Ideas …

•  In order to manipulate growing space effectively, the silviculturist needs to know how it is being utilized currently, and how a growing space manipulation (thinning) will change that

•  Ability to quantify stand growing space utilization leads to sound silvicultural decisions and sound mgt. 37