improving the accuracy of diameter distribution title

1

Title

Improving the accuracy of diameter distribution

predictions by using stand table projection

Meeting: Precision Forestry Symposium

Location: Stellenbosch

Prepared by: Heyns Kotze

Date: 3 March 2014

12 March 2014 Heyns Kotze - PFS PAGE 1

Location

2


Working Circles and Species

Working

Circle

Area

(%)

Species Rotation

(Years)

PSPH

Gum Pulp 72

Eucalyptus dunnii

E. grandis

E. grandis x urophylla

E. grandis x nitens

E. grandis x camaldulensis

...

±8 1389

1667

Pine Pulp 21

Pinus patula

P. elliottii

...

±15 1333

1667

Wattle Pulp 7 Acacia mearnsii ±10 2222

Unthinned, Even-aged, Single species stands

Plans • Annual Plan of Operations (APO) • 3 Year Tactical Plan • 30 Year Long-term Plan


Forest Planning

Growth & Yield Simulator

Compartment Database

Harvest Scheduling & Tactical Planning

Home-grown forest planning systems e.g. MicroForest Similar architecture for • Stand-level G&Y models • G&Y simulators

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Improved accuracy of yield prediction

• Use accurate compartment description: Species, PSPH, Planting Date, etc.

• Use Effective compartment Area as verified from latest orthophotos

• Use a Volume% adjustment factor to cater for damages

• Use applicable Species-level models

• Use Log specification, stump height, log trim and Util top diameter

that reflects business practice

• Use accurate enumeration instead of SI-based defaults

• Calibrate models with stand-level parameters such as:

• Age, TPH, Hdom, BA, DbhStdDev, Dbhmin

• Calibrate the stand table, by using stand-table projection

Plans • Annual Plan of Operations (APO) • 3 Year Tactical Plan • 30 Year Long-term Plan


Forest Planning - Inventories

G&Y Simulator

Compartment Database

Harvest Scheduling

Pre-clearfell Enumeration • Sampling Intensity ~ 5% • ± 20% of area

SI-based defaults • Management level

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• Trees per hectare (TPH) • Basal Area (m2/ha) • Dominant Height (m) • Dbhq (cm) • Util Volume (m3/ha) • MAI (m3/ha/yr)

Stand-level view of a compartment

Size-class variables • Dbh distribution: Number of trees in each Dbh class • Average Ht by Dbh relationship

Size-class view of a compartment

Dbh class (cm)

He

igh

t (m

)

TPH

Fre

qu

en

cy

5

Single tree Stand-level Process

Stand-level projection Growth = f(Age, Hd, TPH, BA)

Physiologically based • Photosynthesis • respiration e.g. 3-PG; Evaluate Climatic effects

Individual tree models Spatial or Non-spatial e.g. SILVA

• Management planning;

• Optmization of regimes.

Understanding

• Inter-tree competition

• Mixed species

Understanding growth

responses to:

• climate & site

Stand table projection

Size class

Projecting stand

structure

Growth modelling approaches

Commercial Planning Scenario Analysis

Group Component Function Graph

Growth Hdom HT2HF3:

TPH NS2CLJ:

BA BA1MR1:

Stand

Structure

Dbh distribution

Weibull MOM

- Dmin:

DMINBHWK:

- Dsdev SDBHWK:

Ave Ht by Dbh HQDBH_DD:

Products Voltaper & Bucking VOLTAPERMB:

Calibration

For SI-based

Assumptions &

BA calibration model

BA1MR1:

Projection Dbh-distribution

projection

Nepal-Summers method

Growth model architecture - unthinned

23

1

113

1

121

2

2

AGEAGE

AGEHD

AGEAGE

AGEHD

133

1

1

12212

100100

AGEAGETPHTPH

1

15

1

141312

1

101

lnlnlnlnexp

AGE

HD

AGE

TPHHDTPH

AGEBA

bRATb DmeanDminD

AGENRSDD RATbRAT 3210

BAAGEDbSd 210

2

2231

21

2

2

10

2 11 IXaIXaXXDBHd ib

1

15

1

141312

1

101

lnlnlnlnexp

AGE

HD

AGE

TPHHDTPH

AGEBA

Dq

DBHHmeanh i

i 210exp1

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Growth modelling approach published in the 2012 South African Forestry Handbook


SI-based growth prediction

For longer term plans, we use SI-based growth prediction.

• Require the growth model to reflect ave behaviour over Age, SQ and Stand density.

Surv% SI Pred

Cal BA

Weibull

Log specification, Greedy bucking algorithm,

Defaults for Stump Ht, Log trim, Util top diameter

• Use stable defaults to calibrate the models.

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Enumeration-based growth projection

For shorter-term plans (APO), we require improved accuracy for:

• Budgeting purposes • Rates for contractor payment • Balancing of man-machine in Tactical Plans

Therefore we use Enumeration based growth projection

Enumeration

• Age

• Dominant Height

• Trees per Hectare

• BA

• Dbh distribution • Minimum Dbh • Standard deviation of Dbh • Unique shape


Enumeration-based growth projection

TPH Hdom BA

Future Stand table

Dbh StdDev

Dbhmin

Observed Stand table

Project

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Dbh distribution ~ Stand table

Dbh-class Midpoint Frequency

3 5.8

4 0.0

5 5.8

6 0.0

7 0.0

8 0.0

9 0.0

10 0.0

11 0.0

12 0.0

13 5.8

14 5.8

15 0.0

16 5.8

17 5.8

18 0.0

19 5.8

20 0.0

21 0.0

22 11.6

23 0.0

24 11.6

25 11.6

....

Total 296

Dbh distribution Stand table


Reconstructing Dbh distribution - Weibull method

To estimate Weibull parameters:

• Method of Moments (Garcia, 1981)

• Input:

• Dbh_min

• Dbh_mean

• Dbh_StdDev

• Estimate these from stand-level

parameters, such as Age, TPH, BA.

Weibull pdf:

• Parameters:

• a ~ location

• b ~ scale

• c ~ shape

• Provides smooth unimodal distributions

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Generalized approach to Stand Table Projection

• Algorithm defined by Nepal and Somers (1992).

• Method requires: a current stand table,

and BA and TPH at a future age

• General diameter growth equation, as defined by Bailey (1980).

• Uses the Weibull parameters of the current age (a1, b1, c1)

and future age (a2, b2, c2).

• Assumes that trees remain in their relative positions to others.


Generalized approach to Stand Table Projection

• The diameter growth equation is used to project the observed stand

table to a future age.

• The future stand table is algorithmically adjusted so that it is

consistent with future BA and TPH.

• Complex and difficult to program

• Illustrated detail with South African data

• (Corral-Rivas etal. 2009, Southern Forests Journal)

• Demo program (STPUtility.exe)

• Implemented in SA Growth & Yield simulators:

• FORSAT (KLF)

• MicroForest Planning System (Syndicate Database Solutions)

• PSAT (Mondi)

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Predicting future Dbh distributions - comparison

Weibull method Stand table projection

Both approaches are consistent with the stand-level growth model,

but the stand-table projection method maintains the structure of the

observed Dbh distribution


Demo software: STPUtility.exe (Input)

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Demo software: STPUtility.exe (Results)


Conclusion

The generalized Stand Table Projection method:

• alternative method to predict future Dbh distributions

• consistent with stand-level growth models

• should provide for more accurate estimates of log products

• because it maintains the shape of observed Dbh distribution

• especially useful for multi-modal or irregular Dbh distributions

Valuable addition to the general stand-level modelling approach

for even-aged single species stands as used in South Africa.

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FORWARD - LOOKING STATEMENTS

It should be noted that certain statements herein which are not historical facts, including, without limitation those regarding expectations of market growth and developments; expectations of growth and profitability; and statements preceded by “believes”, “expects”, “anticipates”, “foresees”, “may” or similar expressions, are forward-looking statements. Since these statements are based on current knowledge, plans, estimates and projections, they involve risks and uncertainties which may cause actual results to materially differ from those expressed in such forward-looking statements. Various factors could cause actual future results, performance or events to differ materially from those described in these statements. Such factors include in particular but without any limitation: (1) operating factors such as continued success of manufacturing activities and the achievement of efficiencies therein, continued success of product development plans and targets, changes in the degree of protection created by Group’s patents and other intellectual property rights, the availability of capital on acceptable terms; (2) industry conditions, such as strength of product demand, intensity of competition, prevailing and future global market prices for the Group’s products and raw materials and the pricing pressures thereto, financial condition of the customers, suppliers and the competitors of the Group, potential introduction of competing products and technologies by competitors; and (3) general economic conditions, such as rates of economic growth in the Group’s principal geographical markets or fluctuations of exchange rates and interest rates. Mondi does not a) assume any warranty or liability as to accuracy or completeness of the information provided herein b) undertake to review or confirm analysts’ expectations or estimates or to update any forward-looking statements to reflect events that occur or circumstances that arise after the date of making any forward-looking statements.

improving the accuracy of diameter distribution title

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