1

Development, Calibration, Evaluation And

Application Of

a Spatially Explicit, Individual-Tree,

Growth And Yield Model

Ian R. Cameron

Azura Formetrics

Kamloops BC

Tree And Stand Simulator

TASS

2

Introduction

TASS Structure and Operation

TASS II

TASS III

Calibration

Individual-Tree Measurements

Plot Measurements

Adaptation to New Silviculture Treatments

and Issues

Model Evaluations

Applications

Outline

3

Introduction

History and Overview

-beginnings 1963 - Ken Mitchell

-historically - spatially explicit models

- Canadian role

- Canadian Forest Service, Yale Univ.

- 1980 - BC Forest Service

- TIPSY

Outline

4

Introduction

TASS Structure and Calibration

TASS II

TASS III

Model Evaluation

Adaptation to New Silviculture Treatments

and Reporting Requirements

Applications

Outline

5

Individual Tree – geometric model of the

crown and bole of individual trees

Spatial – recognizes location of trees in 3D space

Raster Model – 3D growing space

Crown Model

– organ of competition

– metric of growing space

– crowns search the growing space without

calculating inter-tree distances.

Classification

6

Growth and Yield Model

– measure of success is repeating the patterns

of tree dimensions observed in historic yield

experiments and plots.

– intended for application to management

issues.

Classification (cont’d)

7

Growth & Yield PSPs

inventory

monitoring

G &Y Experiments

plot-level statistics

tree-level statistics

crown measurements

branch measurements

upper stem diameters

(taper & form)

Hierarchy of Measurement Detail

8

Individual Tree – destructive analysis

Crowns

Branch extension

- 1st Order

- Higher order

Branch diameters

Foliar Biomass

- Distribution

- Leaf Area & SLA

- leaf anatomy

- leaf morphology

- leaf physiology

Hierarchy of Measurement Detail (cont’d)

9

Individual Tree – destructive analysis

Boles (stems)

Height increment

Ring width and area

Sapwood area

Earlywood – Latewood

Ring density profiles

Cell characteristics

(microfibril angle)

Hierarchy of Measurement Detail (cont’d)

10

TASS Components

- Height Growth

- Branch Growth & Crown Expansion

- Crown Competition

- Tree Mortality

- Crown Volume

- Bole Increment

- Increment Distribution

11

Potential height growth of individual trees

(may be altered by competition)

0 10 20 30 40

Total age (years)

0

5

10

15

20

25 Height (m)

Relative height vigour

12

Measurements of

branch length and

branch growth …

… described by

distance from the

apex

13

Shells of productive crown, integrated as

weighted foliar volume integrated to determine weighted foliar volume

integrated to determine weighted foliar volume

i Hgi Wi WiHgi

1 0.55 1 0.55

2 0.55 0.86 0.47

3 0.5 0.75 0.38

4 0.3 0.63 0.19

5 0.5 0.4 0.2

Sum: 1.59

FV = CA* WiHgi = 31.4*1.59 = 50 cu.m.

Crown Volume

Crown area = 31.4 sq.m

14

Crown Competition

space is occupied, "branches" die, and crowns lift space is occupied, "branches" die, and crowns lift

space is occupied, "branches" die, and crowns lift

15

Mortality based on

- degree of overtopping

- size of crown relative to size of tree

overtopped

tree

Live trees

16

0 50 100 150 200 250

Foliar volume (cu.m)

0

0.1

0.2

0.3

0.4 Bole increment (cu.m)

Bole increment

With other modifiers for competition effects

17

0 1 2 3 4 5 6 7 8 9 10 11 12 13 -1

Length below top (m)

0

1

2

3

4 Area increment (sq.mX1000)

Butt swell

Area Increment from Tree Measurements

Crown base

18

Area Increment and Diameter Increment

From Tree Measurements

0 1 2 3 4 5 6 7 8 9 10 11 12 13 -1

Length below top (m)

0

1

2

3

4 Area increment (sq.mX1000) Diameter increment (cm)

area

diameter Crown base

19

Average values by source and crown class

0.0 0.5 1.0 -0.5 -1.0

Relative distance to foliar centroid

0.2

0.3

0.4

0.5

0.6

0.7

0.8 Relative density

Latewood

Earlywood

0.4

0.5

0.6

0.7

0.8

0.9

1.0 Earlywood area inc./total area inc.

Proportion Earlywood

Center of foliar biomass Top Base

Crown class (no. trees)

Intermediate (3) Codominant (3) Dominant (5) Open grown (7)

20

Stem

Profile

Juvenile

Wood

Clear Wood

Mature

Wood

21

22

Simulated Lumber

Planting

Density

330/ha

820/ha

2500/ha

2.08 rings/inch

2.17 rings/inch

2.50 rings/inch

23

Introduction

TASS Structure and Calibration

TASS II

TASS III

Model Evaluation

Adaptation to New Silviculture Treatments

and Reporting Requirements

Applications

Outline

24

TASS III

3-year Project (2005/06 to 2007/08)

Integration of Components Previously Developed

- Redesigned Raster Grid

- VISTAS visualization

- tRAYci light model (Brunner 1998)

New Components

Graphical User Interface

Carbon-Balance structure

Updates

Crown shyness

General Release

25

TASS Grid

Square columns

Typically

20 cm x 20 cm

TASS II

One canopy layer

Per grid column

26

TASS III Grid

TASS III

- multiple layers

per grid column

-overlaps permitted

(interlocking crowns)

27

TASS with and without tRAYci light model

TASS II

TASS III

28

VISTAS

3D Visualization

OpenGL Graphics

Integrated

graphic and text

reporting

Analysis of Stand

Structures

29

30

Without crown shyness With crown shyness

Crown Shyness

31

Adapting to New Treatments, Pests and Issues

How are tree components affected?

- Height Growth

- Branch Growth & Crown Expansion

- Crown Volume

- Bole Increment

- Increment Distribution

- Crown Competition

- Tree Mortality

32

Adapting to New Treatments, Pests and Issues

How are tree components affected?

- Height Growth

- Branch Growth & Crown Expansion

- Crown Volume

- Bole Increment

- Increment Distribution

- Crown Competition

- Tree Mortality

Example: Genetic Gain

33

Adapting to New Treatments, Pests and Issues

Example: Armillaria Root Disease

How are tree components affected?

- Height Growth

- Branch Growth & Crown Expansion

- Crown Volume

- Foliar Biomass

- Bole Increment

- Increment Distribution

- Crown Competition

- Disease spread – root systems

- Tree Mortality

X

X X

Special Version of TASS

34

Introduction

TASS Structure and Calibration

TASS II

TASS III

Adaptation to New Silviculture Treatments

and Reporting Requirements

Model Evaluation

Applications

Outline

35

Total volume/ha vs height

0 2 4 6 8 10 12 14 16 18 20

Top Height (m)

0

50

100

150

200

250

300

350

400 Total volume (cu.m/ha)

7907

3951 1975

988

494

Gregg Burn - Average over all sites TASS

36

Diameter distributions at age 40

Site 2 vs. TASS simulations Site 2 vs. TASS simulations

Site 2 vs. TASS simulations

<2.5 5 10 15 20 25 30 35 40

DBH class (cm)

0

1

2

3

4

No. trees/ha (Thousands)

Gregg Burn

TASS

494/ha 988/ha

1977/ha 3954/ha

7907/ha

37

Introduction

TASS Structure and Calibration

TASS II

TASS III

Adaptation to New Silviculture Treatments

and Reporting Requirements

Model Evaluations

Applications

Outline

38

Silvicultural Treatments

Planting

Pre-commercial thinning

Commercial Thinning

Fertilization

Pruning

Genetic Gain

Species

Douglas-fir

Western Hemlock

Western Redcedar

Sitka Spruce

Lodgepole Pine

White Spruce

Red Alder

Trembling Aspen

Engelmann Spruce

Subalpine Fir

Pests

Sitka spruce terminal weevil

Armillaria root disease

Phellinus root disease

39

Challenges in Application

Bias Associated With the Calibration Data

- experimental installations

- subjectively located plots

- mortality, increment losses and damage

TASS yields reflect the potential, even if we are

accounting for density effects.

40

Challenges in Application

Spatial Coordinates for Trees

Stem maps are rare.

Assume distributions at stand initiation

- plantings tend to be regular

- natural regeneration can be added in a variety

of spatial arrangements … but the user

must choose the one they want.

- simulate wide range of alternatives to assess

the sensitivity

- measure stem maps for case studies of

interest.

41

Challenges in Application

Spatial Coordinates for Trees

Initiating mature stands is problematic

Defining the joint distributions of spatial

arrangement and tree size for a mature stand is one

of the most difficult problems in quantitative forestry

– simply choosing random coordinates is

unsatisfactory.

A partial solution -- approximate mature stand

conditions by iterating over a range of initial

conditions.

42

Stand-Level Silviculture Decisions

Best application of TASS because of close link to

the type of calibration

Emphasis on response to treatment

Calibration bias less of an issue

- ranking of alternatives

- relative responses

More comfort with requisite assumptions on

spatial distributions

43

Yield Curves for Forest Management Planning

Bias issue must be addressed by:

- yield reductions (Operational Adj. Factors)

when primary focus on volume.

OR

- explicit identification of factors that contribute

to the bias:

•spatial distribution of trees, with emphasis

on “holes”

• non-productive areas

• forest pests

44

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Perc

ent C

om

positio

n B

ryoria

0 5 10 15 20 25 30 35 40

Years Since Logging

< 10m 2 /ha

10 - 20m 2 /ha

>20 m 2 /ha

0

5

10

15

20

Heig

ht of A

lecto

ria/B

ryoria T

ransitio

n

0 5 10 15 20 25 30 35 40

Years Since Logging

< 10m 2 /ha

10 - 20m 2 /ha

>20 m 2 /ha

B)

A)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Perc

ent C

om

positio

n B

ryoria

0 5 10 15 20 25 30 35 40

Years Since Logging

< 10m 2 /ha

10 - 20m 2 /ha

>20 m 2 /ha

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Perc

ent C

om

positio

n B

ryoria

0 5 10 15 20 25 30 35 40

Years Since Logging

< 10m 2 /ha

10 - 20m 2 /ha

>20 m 2 /ha

0

5

10

15

20

Heig

ht of A

lecto

ria/B

ryoria T

ransitio

n

0 5 10 15 20 25 30 35 40

Years Since Logging

< 10m 2 /ha

10 - 20m 2 /ha

>20 m 2 /ha

0

5

10

15

20

Heig

ht of A

lecto

ria/B

ryoria T

ransitio

n

0 5 10 15 20 25 30 35 40

Years Since Logging

< 10m 2 /ha

10 - 20m 2 /ha

>20 m 2 /ha

< 10m 2 /ha

10 - 20m 2 /ha

>20 m 2 /ha

B)

A)

From Lewis (2004)

Masters thesis,

Simon Fraser U.

Transition from

Bryoria to Alectoria

descends in the tree

after partial cutting

45

STS

25m

50m

100m

20%* 40% 60% 80% T

rea

tme

nt T

yp

e

Percent Removal

Factorial design of TASS simulation experiment

46

ESSF Simulations Pre-Cutting Conditions

PACL at 0.5m above ground level VISTAS representation

Engelmann Spruce

Subalpine Fir

ESSF Simulations 60% removal – Single Tree Selection

ESSF Simulations 60% removal – 25m x 25m Patches

47

0m

5m

10m

15m

1 x 1m “cell”

Gra

die

nt

of

Aver

age

PA

CL

Valu

es

20m

Live Foliage

Dead Foliage (0-15 yr.)

Dead Foliage (16- 40 yr.)

Dead Foliage (>40 yr.)

Selection

Harvest

PACL

Values0-15 16-30 31-45 46-60 60-80 >80

ESSF Simulations

Zones for live & dead branch

48

Concluding Remarks

There are inherent advantages and disadvantages to each

of the different spatiophysical model types. Useful models

can be constructed from any of these structures. The

merits of the resulting model will depend on the many

other decisions made about the architecture within that

spatiophysical framework. Model evaluation is an

essential component of the model building process and

will help users differentiate the models that are useful from

those that are not.