Measures of productivity - Oregon State University · 322 Measures of productivity • Determinants of productivity ... Douglas-fir tree in Table 2 took 62 years to grow from breast

FOR322 Measures of productivity

• Determinants of productivity• Site index

• Guide curve method• Stem analysis method• Repeated measurement method• One vs. two equation systems• Determining site index

• Growth intercept • Plant indicators• Soil-site relationships


Productivity is the inherent capability of

the land to produce wood volume or tree

biomass of the specified species.

GPP = gross primary productivityNPP = net primary productivity

= total dry matter production by primary producers (plants)

= GPP – respiration


STEM WOOD

TREE BIOMASS

FOREST

BIOMASS

NPP

GPP

RESPIRATION


Determinants of productivity• Soil

• Nutrients

• Water holding capacity

• Water table level

• Depth

• Temperature

• Texture

• Climate

• Daytime temperature

• Nighttime temperature

• Rainfall (amount and timing)

• Humidity (vapor pressure deficit)

• Solar radiation

• Length of growing season

• Extreme events (temperature, vapor pressure deficit, . . .

• Soil micro-organisms, including bacteria and mycorrhizae


Swenson and Waring (2005)

Estimates of

regional site

index from an

ecophysiological

growth model,

3PG


Swenson and Waring (2005)

One driving

variable for the

ecophysiological

growth model,

3PG, is soil N.

Soil N is

integrated with

climatic data and

other soil

variables like

water holding

capacity


Properties of an "Ideal" Measure of Productivity

1. The measure should be very highly correlated with

potential, maximum wood volume (or biomass) for the

stand (e.g., maximum MAI).

2. The measure should be independent of stand density.

3. The measure should be independent of thinning regime

(i.e., manipulations of stand density).

4. The measure should be specific to the species or

genotypes that convert site resources into biomass


The most common measures of productivity

applied in forest management are:

1. Site Index

2. Growth Intercept

3. Plant Indicators

4. Soil-Site

5. Net photosynthesis or NPP from an

ecophysiological model


Site Index:

The total height of the dominant /codominant

component of a stand at a specified base age

King’s (1966)

50-yr site

index for

coastal

Douglas-fir

Base age

50 yrs Site index

curves for 50

to 160 ft at 50

yrs


Base Age:

The reference age for determining site index.

Base age can be expressed as either a total,

breast height, or plantation age, in years.

The base age is often set near the average

rotation length for the species.

Common base ages in the western United States

are 50 and 100 years. In the South, a base age

of 25 years is not unusual.


Flewelling et al. (2001) developed site index

curves of base age 30 for intensively managed

Douglas-fir stands


Site Index Equation:

Predicts site index from age (either

total, breast height or plantation age)

and dominant height.

Depending upon the equation, age and

dominant height can be either individual

tree values or an average for the stand.


Dominant-Height-Growth Equation:

Predicts dominant-height from age (either

total, breast height, or plantation age) and site

index.

Depending upon the equation, age and

dominant height can be either individual tree

values or an average for the stand.


Anamorphic Equations:

Exhibit the property that the shape of the

height-age curve for a particular site index is the

same regardless of the value of the site index.

Therefore, all site index curves are proportional to

each other, the difference between two curves

being proportional to the ratio of their site indices.


Polymorphic Equations:

Exhibit the property that the shape of the

height-age curve for a particular site index is

different from that of other site indices.

Therefore, the difference between two curves

is not proportional to the ratio of their site

indices.


Three common methods of constructing

site index equations have been applied:

1. Guide Curve Method

2. Stem Analysis Method

3. Remeasurement Method


Guide curve method for constructing site index equations

McArdle - Bulletin 201 site curves

Base age 100 years

100 yrs


So how is it done?


• Pairs of height and age measurements are collected

from a large number of sampled trees or stands

• The data points corresponding to the height-age pairs

on plotted, age on X-axis and height on Y-axis

• A guide curve is drawn through the data, or a

regression equation is fitted to the data

• The height at the desired base age for the guide

curve is determined



Example from class notes: inland Douglas-fir from Brickell (1968)

Guide curve crosses 70 ft at 100yrs.

To get site index 50, multiply the

guide curve by 50/70.


So how is it done? (cont’d)


• Curves for specific site indices (e.g., increments of 10

or 20 feet) are determined by multiplying the guide

curve points by the ratio of the desired site index to

the guide curve site index:

HA,S = HA,G(S/SG)

HA,G = Dominant height at age A from the guide curve

HA,S = Dominant height at age A for site index S

SG = Site index of the guide curve

S = Desired site index


Example from class notes: inland Douglas-fir from Brickell (1968)

Guide curve crosses 70 ft at 100yrs.

To get site index 50, multiply the

guide curve by 50/70.


Guide curve method is very handy for forest

types and geographic regions with little or no

history of permanent plots, as was true almost

everywhere during early days of forestry in

the United States.

• Bulletin 201 – The yield of Douglas-fir in

the Pacific Northwest (McArdle et al. 1949)

• Bulletin 354 – Preliminary yield tables for

second-growth stands in the California pine

region (Dunning and Reineke 1933)


A useful reference of the literature on site index

and dominant height growth curves was

produced in 1995 by David Hann:

Hann, D.W. 1995. A key to the literature presenting site

index and dominant height growth curves and equations

for species in the Pacific Northwest and California.

Forest Research Laboratory, Oregon State University,

Corvallis. Research Contribution 7.

pdf is posted on T:\Teach\Classes\FOR322\publications








• Small sample of dominant/codominant trees is felled

and sectioned at short intervals (e.g., 4-8 ft)

• At top of each section measure

• Height from ground

• Ring-count age in years

• Reconstruct past height growth of each tree and its

interpolated height (site index) at desired base age.

(Note that the sample trees have to be at least as old as

the desired base age.)

• Apply regression analysis to develop

• site index equations

• dominant height growth equations

Stem analysis method for constructing site index equations


Cross-sections showing ring counts on Austrian black pine collected by

Dr. Philippe Dreyfuss of INRA, Avignon, France

14

rings

68 rings

116 rings


Stem profile

reconstructed by

stem analysis.

Ring counts and

diameters taken at

heights marked by

arrows.

Allow

reconstruction of

past height growth

of tree.



Annual height growth of dominant Austrian black

pine reconstructed by stem analysis.


Cumulative height growth of dominant Austrian

black pine reconstructed by stem analysis.

base age 100

yrs total age

base age 50

yrs total age


Example: Douglas-fir tree in Table 2 took 62 years to grow from breast

height to current total height of 160.4 ft. So, breast height age

is 62 years.


BHAi = RCbh – RCi

where

BHAi = Breast height age for the ith

section height

RCbh = Ring count at breast height

RCi = Ring count at ith section

height



4953

4950)5.1309.138(5.130SiteIndex

=130.5 +(8.4)(1/4)

=130.5 + 2.1

=132.6 ft

50

To get height at base age of 50

years at breast height:


Cumulative

height

growth for

sectioned

tree.

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70

Tota

l he

igh

t (f

t)

Breast height age (yrs)

Tree 370-1-6


Stem analysis data can be used to develop dominant

height growth equations that are either anamorphic or

polymorphic, depending on the selected statistical

model .

Most are polymorphic, because the detailed analysis

of individual tree growth reveals that dominant height

growth patterns among different site indices are in

fact polymorphic, i.e., not proportional across full age

range.


Examples of equations developed from stem analysis methods:

• Douglas-fir

• Second growth in western WA (King 1966)

• High elevations in OR & WA (Curtis et al. 1974)

• Eastside of Cascades in OR & WA (Cochran 1979)

• Western Montana and northern Idaho (Monserud 1984)

• Dry sites on Willamette N.F. (Means and Helm 1985)

• Southwestern Oregon (Hann and Scrivani 1987)

• Noble fir

• High elevations in Cascades of OR & WA (Herman et al. 1978)

• Ponderosa pine

• Eastside of Cascades in OR & WA (Barrett 1978)

• Northern California (Powers and Oliver 1978)

• Southwestern Oregon (Hann and Scrivani 1987)

• Other examples in Hann (1995) Key to the literature presenting site

index and dominant height growth curves and equations for species

in the Pacific Northwest and California


Summary of Douglas-fir site index equations

developed from stem analysis

Source Sample size Upper age

Curtis et al. (1974) 52 trees 400 yrs

Means and Helm (1985) 27 trees 280 yrs

Hann and Scrivani (1987) 89 trees 136 yrs

Means and Sabin (1989) 55 trees 120 yrs

King (1966) 85 plots 130 yrs

(850 trees)

Total 223 trees


Geographic range of Douglas-

fir site index equations

developed from stem analysis

General conclusion:

Numerous studies of site index in

region, but studies have :

• Small sample sizes

• Restricted age range

• Restricted geographic range








• Sample of stands is selected for installation of permanent

plots

• Dominant trees are identified, typically the largest 40 trees per

ac by dbh

• Initial heights and breast height age measured; or, plantation

and/or seedling age is recorded.

• Total height is measured periodically, and ages computed from

initial age to yield height-age pairs

• The more the frequent measurements and the longer the

duration of the permanent plots, the better the resulting

dominant height growth and site index equations

Remeasurement method for constructing site index equations


• Resulting equations can be either anamorphic or polymorphic,

depending on choice of the statistical/mathematical model

• As with equations developed from stem section data, most are

polymorphic because dominant stand height development

among different site indices is generally polymorphic.

• Note: King’s (1966) widely applied site index

curves/equations are most accurately described as being

constructed by stem analysis: height-age pairs were

determined by measuring heights to successive whorls on

Douglas-fir. HOWEVER, dominant height-age pairs were

averaged for trees on a plot, so equations apply to top height

development of plots vs. individual dominant trees

Remeasurement method for constructing site index equations


Height growth implied

by Flewelling et al.

(2001) site index

curves (H40) based on

remeasurement of

Stand Management

Cooperative plots.


Examples of equations developed by the

remeasurement method:

• Douglas-fir

• Second growth in northwestern OR & western WA

(Bruce 1981)

• Young plantations in northwestern OR & western WA

(Flewelling et al. 2001)

• Western hemlock

• Southwestern BC, western WA & northwestern OR

(Bonner 1995)

FOR322

End 13 February 2012

Measures of productivity


Comparison of the three methods for constructing

dominant height growth and site index equations

Assumptions built into the guide curve method:

1. All site indices are equally represented across

the full range of stand ages.

2. The shape of the height-age curve is

independent of site index.

3. The frequency and severity of height damage

that the sampled plot experienced in the past

are typical of the population to which the

equations will be applied.


Violation of any of the three assumptions built into

the guide curve method can result in biased site

index and dominant height growth curves.

1. Example of UNEQUAL representation of all site

indices across the full range of stand ages.


Equal

distribution

of all site

indices

across all

ages

High

Medium

Low


Lack of

plots at

high site

indices at

later ages


Lack of

plots at

high site

indices at

later ages


Assumption 1:

Violated if historical trend of harvesting the highest

sites first (higher volumes), resulting in over-

representation of high sites at young ages and

under-representation of high sites at old ages.

Declining site index over age (e.g., Monserud

1984) would make dominant height growth curves

too high below the base age and too low above the

base age, resulting in flatter growth curves.


Monserud guide

curves vs. stem

analysis curves

fitted to same

dataset.


Assumption 2:

REALITY: Objective statistical analysis of data

from stem analysis and plot remeasurement

typically result in polymorphic curves forms.

This result suggest that assumption 2 is probably

not biologically realistic.


Assumption 3:

Trees which appear perfectly sound and healthy

while standing often exhibit hidden height damage

when sectioned (e.g., 51 out of 140 Douglas-fir in

southwestern Oregon).

Single measurement data used to develop guide

curves usually do not include information on

frequency and severity of past height damage, so it

is impossible to assess whether or not the

modeling data are typical.


• Elimination of sectioned trees with any past height

damage

• Under-estimate site index if applied to dominant

trees with hidden height damage

• Over-predict dominant height growth of real stands

with typical frequency of height damage

• All sample trees must be older than base age

• Resulting height growth curves describe

population of trees that survive to older ages, so

may not be representative of stands at young ages

• “Shooters” with rapid early growth, “stayers” with

slow early growth and faster later growth

Problems associated with stem analysis method


Base age

Heig

ht

Age

shooters

stayers

Fitted curve misses

shooters so

underestimates height

growth at young ages


• Advantages:

• Avoids problem of shooters and stayers if

remeasurements cover both the shooter phase and

stayer phase of stand development.

• Represents the top height development of stands that

experience the same frequency and severity of top

damage as occurred in sampled plots.

• Disadvantages:

• More subject to error in height measurements than stem

analysis

• Requires large investment in time and money to collect

adequate data.

• Historically restricted to even-aged stands of

commercially important species.

Relative merits of remeasurement method


X on Y

Y on X

Y (

SIT

E IN

DE

X)

X (H40)

Two-equation site index/H40

system (AGE fixed)


• Site index curves constructed with top height on Y-axis and

age on X-axis; site index determined by matching an

observed height-age pair to nearest or interpolated site

index

• Early site index equations similarly expressed top height as

function of age; solve equation for site index for a given

height-age pair

• In regression analysis get different equation for:

• Site index = f( age, top height)

• Top height = g( age, site index)

• Solution has been to develop two separate equations

One- vs. two-equation systems for site index

and dominant height growth


Dominant height growth

curve for Douglas-fir in

southwestern Oregon

(Hann and Scrivani 1987)


Site index curve

for Douglas-fir in

southwestern

Oregon (Hann

and Scrivani

1987)


• Hann and Scrivani (1987) found that estimating site index

from the dominant height growth equation gave better

predictions of future height growth rates than using the two-

equation system

Interesting results of two-equation systems


1. For what kind of stands is the application of the site index

curves appropriate?

2. What kind of trees should be selected for measurement of

site index?

3. How many trees should be measured in the stand?

4. What age (i.e., total, breast height or plantation) does the

site curve use?

5. How should multiple species stands be measured?

6. Should the heights and ages be averaged for the stand

before using the site index equation or should site index be

determined for each tree and the site index values averaged

to determine average stand site index?

Determining site index for a stand


1.Establish a fixed area plot that encompasses 50 Douglas-fir

trees that are 1.6 inches in dbh or larger.

2.Measure total height and breast height ages on the 10 trees

with largest diameter.

3.Compute the average height and age of the 10 trees.

4.Use these average values to estimate site index.

King’s (1966) method:


1. Sort sample trees by decreasing DBH

2. Accumulate expansion factors

3. Find tree at which cumulative expansion factor equals or

exceeds 40 trees per acre

4. Determine each tree’s weight (tpa) for computing H40

(height of 40 largest trees per ac)

- For all but the smallest tree, this contribution will be the

expansion factor

- For the smallest tree, this contribution will be the amount

of its expansion factor need to total 40 trees per ac

5. Compute H40 as weighted mean using expansion factors

as weights

Example of King’s (1966) method:


Expansion Cumulative Contribution

DBH HT Factor to H40

13.5 75.2 15.00 15.00 15.00

12.5 76.8 10.00 25.00 10.00

11.4 73.8 30.00 55.00* 15.00#

10.6 71.8 55.00 110.00 0.00

9.5 69.9 80.00 190.00 0.00

8.6 67.5 100.00 290.00 0.00

7.5 64.5 100.00 390.00 0.00

6.5 61.6 150.00 540.00 0.00

5.5 57.2 155.00 695.00 0.00

4.6 52.0 180.00 875.00 0.00

3.5 45.2 75.00 950.00 0.00

3.0 39.4 15.00 965.00 0.00


H40 = [(15.0x75.2) + (10.0x76.8) + (15.0x73.8)]/40.0

= 3,003.0/40.0

= 75.075-feet

The breast height age (Ab) of example stand was:

23-years.


Calculation of King's (1966) site index:

S = 4.5 + (2500.0 X6)/(X7 - X8)

Where,

S = Site index of the stand, feet

X6 = 0.109757 + 0.00792236 Ab + 0.000197693 Ab2

X7 = Ab2/(H40 - 4.5)

X8 = -0.954028 + 0.0558178 Ab - 0.000733819 Ab2

Site index = 4.5+[2500(0.396550877)]/[7.495572086-(-0.058408851)]

= 135.7 feet at 50 years


Calculation of King's (1966) dominant height growth:

H40 = 4.5 + Ab2/(X1 + X2 Ab + X3 Ab

2)

Where,

X1 = -0.954028 + 0.109757 [2500./(S-4.5)]

X2 = 0.0558178 + 0.00792236 [2500/(S-4.5)]

X3 = -0.000733819 + 0.000197693 [2500/(S-4.5)]

Predicted H40 at age 70 would be:

H40=4.5+702/(1.13737825+0.206777404(70)+0.003033197(702)

H40=165.3 feet


1. Because height growth is highly correlated with volume

growth, height at an index age should be highly

correlated with maximum potential volume in stands

without stockability problems.

2. For a number of species, height growth of dominant trees

is relatively unaffected by stand density. However, for

some species dominant height growth is affected by

density.

3. Height growth rate of a specified species is usually

unaffected by the species composition of the stand.

Advantages of site index:


1. Site index values do not allow easy comparison of productivity

potential between species. Different base ages may have

been used for each species, or each species may approach

different maximum size-density relationship which would result

in different potential volume for a given site index.

2. It is difficult to apply site index in mixed species stands.

3. It is difficult to apply site index in uneven-aged stands because

many dominant trees have not been free growing throughout

their life spans.

4. In stands with stockability problems, site index may not be

highly correlated with maximum potential volume.

Diadvantages of site index:


5. Site index may change over time due to changes in climate, or

to treatments such as fertilization, drainage of soils, or

introduction of genetically improved trees.

6. The measurement of height and age and the subsequent

calculation of site index can be complicated, resulting in

substantial estimation error.

7. Site index equations are usually very imprecise at young ages

(under 20 years).

8. Site index equations cannot be applied to areas that currently

have no trees.

9. Site index should not be applied in high-graded stands or

stands that have been thinned from above (removing all

dominants).

Disadvantages of site index (cont’d):


Uses a measure of the periodic height growth rate

near breast height for dominant trees as an

indicator of productivity.

Growth intercept method


• Periodic height growth rate is determined by measuring

the distance between a specified number of whorls (or,

the length of a specified number of internodes).

• The method can only be applied to species with distinct

whorls.

• The number of internodes used varies between three and

five depending upon the study.

• Which internodes to use for the length measurement also

varies between studies and is usually defined in relation

to breast height.


Measure distance

between nth and

(n+i)th whorl above

breast height,

where i= 3, 4, 5

Growth intercept

method


The growth intercept value can be used to predict

site index by the relationship:

Site Index = b0 + b1(Growth Intercept Value)

As an example, Powers and Oliver (1978)

presented the following equation for ponderosa

pine in northern California growing on soils other

than schist inceptisols:

S = 21.94 + 8.68(HI)


HI = height increment

between first 5 whorls (4 yrs)

above breast height

Measure distance

between nth and

(n+i)th whorl above

breast height,

where i= 3, 4, 5

Growth intercept

method


• Advantages of Growth Intercept Method

• Some feel that the method is superior to standard site index

methods for determining productivity of young stands.

• Growth intercept is generally considered to be easier to

measure than the total height and age values needed to

estimate site index directly.

• Disadvantages of Growth Intercept Method

• The method is based only on early height growth rate which

may not be representative of the rate that can be expected

throughout the tree`s lifetime.

• The method can be more easily influenced by relatively

short term climatic fluctuations because of the relatively

short growth period length.

Advantages and disadvantages of growth intercept:


The presence of certain overstory and/or understory plant

species to indicate productivity is based on the proposition

that these plants integrate the environmental conditions that

determine potential productivity of the site.

Habitat type or plant association can be correlated with site

index; however, a substantial range in site indices can also

be observed on a given habitat type or plant association.

Therefore, other topographic, physiographic, geologic and/or

landform information is often used to further refine the

estimator of productivity (e.g., slope, aspect, elevation).

Plant Indicators


Carmean (1975) lists the following reasons why plant indicators

have not been more widely used as productivity variables in the

United States:

• Topographic, geologic and soil features often explain the

same site characteristics as plant indicators.

• Overstory species composition can affect the vigor and

composition of the understory, even on similar soils.

• Overstory density can affect the abundance, vigor and

composition of the understory.

• Overstory trees are affected by the characteristics of soil

horizons deeper than those affecting the understory.

• Many understory species die back during winter making their

use as indicators difficult or impossible during that time.

Plant Indicators


Plant indicators have also been used to refine dominant height

growth and site index equations.

For example, it has been shown that the dominant height

growth and site index equations for Douglas-fir (Monserud

1984) in northern Idaho and western Montana differ by habitat

type.

Differences by habitat type have also been found for mountain

hemlock in the Cascade Mountains of Oregon and for

Douglas- fir in the Coast Range of Oregon.

Plant Indicators


Recognizing that soil properties are one of the basic factors

affecting productivity, there have been a large number of studies

that have related soil properties to a measure of stand

productivity.

Most of these studies have predicted site index as a function of

soil attributes.

Often these equations also contain variables related to

topographic, physiographic, geologic and/or landform attributes.

Soil-site relationships


For example, Steinbrenner (1979) reported the following

equation for predicting site of Douglas-fir index growing in

western Oregon on sites receiving less that 60 inches of annual

precipitation:

S = b0 + b1(ED)2 + b2(PR)3 + b3(SL) + b4(EL)(POS)

+ b5(EL)(SL) + b6(TC)(DA) + b7[(TC)(DA)]2 (R2=0.74)


S = King’s site index ED = effective soil depth

PR = precipitation SL = slope percent

POS = position on slope EL = elevation

TC = total clay DA = depth of A horizon


Carmean (1975) claims that "most of the successful soil-site

studies explain perhaps 65-85% of the variation in tree height,

or site index...."

However, Monserud et al. (1990) found that:

• Physiographic variables and plant indicators alone could

explain 42% of the variation in Douglas- fir site index in

northern Idaho and western Montana

• Soil variables alone could explain only 16% of the variation in

site index

• The addition of soils variables to physiographic and plant

indicator variables explained a total of 49% of the variation

(7% over the physiographic and plant indicators alone).


FOR322

End 6 February 2015

Measures of productivity

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Measures of productivity - Oregon State University · 322 Measures of productivity • Determinants of productivity ... Douglas-fir tree in Table 2 took 62 years to grow from breast