Amaro A., Reed D., Soares P. (editors) Modelling Forest Systems

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66 A.C. Almeida et al.

Methodology

We used the process-based model 3-PG (physiological principles in predicting

growth), (Landsberg and Waring, 1997) to predict the potential productivity of 19

regions in eastern Brazil, lying between 17° 25 S and 20° 05 S, covering 170,000 ha

of eucalypt plantation (E. grandis Hill ex. Maiden hybrids) (see Fig. 6.1). The regions

were deﬁned based on meteorological measurements made by automatic weather

stations. Mean annual increments estimated by the model for a 6-year rotation were

compared with available observations made annually in permanent sample plots

(PSPs). The forest areas used in the comparison were those planted in 1995, which

had PSPs during the rotation. They represented 10 of the 19 regions and included

213 PSPs.

For the same area, using PSP measurements, we developed an empirical

owth and yield model called

E-GROW ARCEL. The two models have been linked to

allow the prediction of forest productivity and wood products under different envi-

ronmental conditions. The link is based on the MAI at age 6 years (MAI

). There is

a robust relationship between MAI

and SI – deﬁned to be the mean dominant

height at age 5 years – derived from

E-GROW ARCEL. Once 3-PG has provided the

MAI

values, this empirical relationship estimates the SI that is applied in E-GROW

ARCEL

to predict growth and yield at stand structure and product proﬁle levels.

PG model structure

The 3-

PG model is a simple process-based model of forest growth. It requires few

parameters, climatic data inputs, a basic knowledge about the local soil water-

holding capacity and an indication of soil fertility. The model consists of ﬁve sim-

Fig. 6.1. Location of Aracruz Celulose S.A. eucalypt plantation and automatic weather station network.

07Amaro Forests - Chap 06 25/7/03 11:05 am Page 67

67 Linking Process-based and Empirical Models

ple submodels: these describe the assimilation of carbohydrates, the distribution

of biomass between foliage, roots and stems, the determination of stem number,

soil water balance, and conversion of biomass values into variables of interest to

forest managers (Sands and Landsberg, 2002). The time step is monthly and the

main outputs are: gross primary productivity (GPP), net primary productivity

(NPP), leaf area index (LAI), mean stem diameter at breast height (DBH), basal

area (BA), standing biomass (partitioned into foliage, stem and root), MAI and

stem volume.

PG differs from other process-based models because it incorporates important

simpliﬁcations to some well-known physiological processes and can be used as a

practical tool in forest management. Waring and McDowell (2002) described these

simpliﬁcations as: (i) constant ratio of net primary production to gross photosynthe-

sis (Pn/Pg); (ii) canopy conductance approaches a maximum above an LAI of 3.0;

(iii) the ratio of actual/potential photosynthesis decreases in response to the most

estrictive (monthly) environmental limitation; (iv) the fraction of production not

allocated to roots is partitioned among foliage, stem and branches based on species-

speciﬁc allometric relationships with tree diameter; (v) canopy quantum efﬁciency

(α

) is assumed to increase linearly with soil fertility.

PG has been tested for forest species in different countries (see Landsberg et

al., 2000, 2003; Dye, 2001; Sands and Landsberg, 2002).

E-

GROW ARCEL model structure

E-GROW ARCEL is an implicit model, based on the recovery of Weibull distribution

parameters by diameter class. It includes a set of stand models to estimate dominant

height, mortality, basal area, DBH variance, individual tree height and stem taper.

Integrating basal area generated from two levels of resolution (diameter distribution

method and stand-based model) increases the system reliability; following method-

ology presented in Scolforo (1998).

E-GROW ARCEL allows predictions and projection estimates. Prediction refers to

growth and yield based on early stage information, and projection means estimation

using data from forest inventory over time. The model also provides simulation of

stand growth and yield under a solid wood regime.

The basic

E-GROW ARCEL inputs and outputs are:

Inputs

● Stand basic information: genetic material, management regime.

● Forest information: stand age, dominant height, mean diameter, diameter coef-

ﬁcient of variation, tr

ees per hectare and basal area.

● Deﬁnition of the projection age.

Outputs

● Estimation of dominant height, stem density, basal area, diameter variance and

minimum diameter

● Weibull a

, b and c recovered parameters and diameter distribution estimation.

● Total height estimation for each diameter class.

● Merchantable volume estimation for each log class deﬁned by log length and

small end diameter

07Amaro Forests - Chap 06 25/7/03 11:05 am Page 68

68 A.C. Almeida et al.

Data

Used in 3-pg model

The 3-

PG model was rigorously tested against data from an experimental catchment

site before applying it across landscapes. Measurements at the catchment site pro-

vided information about biomass allocation, monthly growth rates, plant nutrition

and water balance.

The catchment area is 286 ha, of which 190 ha are covered by eucalyptus planta-

tions and 86 ha by the original tr

opical rainforest (Mata Atlˆantica), the remainder

being roads. The topography of the plantation area is ﬂat, while the tropical forest

covers the hilly drainage area of the system. Measurements have been made in this

area since 1993 and include:

● Weekly soil moisture measurements in 16 tubes using neutron probe in the

ﬁrst 2.8 m.

● Weekly water table level in ﬁve piezometers.

● Monthly plantation growth in 16 PSPs including different genetic material.

● Three automatic weather stations measuring precipitation air temperature, rela-

tive humidity

, global solar radiation, net radiation, PAR (photosynthetically

active radiation) , and wind speed and direction.

● Monthly LAI using a plant canopy analyser instrument calibrated against

destr

uctive samples taken annually.

● Annual biomass allocation in three trees for each genetic material including

stem, bark, branches, foliage and r

oots.

● Monthly litter fall dry mass in 35 traps.

● Annual stomatal conductance in ﬁve genotypes.

The PSPs were well distributed across all regions; however, the area planted in

1995 cover

ed ten regions only. To calibrate 3-

PG for other regions we used the avail-

able information about soil water-holding capacity and soil fertility from soil sur-

veys at scale 1 :10,000. The automatic weather station network provided the monthly

rainfall, solar radiation, vapour pressure deﬁcit and temperature data used in 3-

PG.

Used in

E-GROW ARCEL model

E-GROW ARCEL was developed using data from 1010 PSPs, covering the range of ages,

SI and management conditions faced by E. grandis hybrid stands across Aracruz

plantations. The measurements included upper-stem diameters at different ages in

different regions, SIs and stem densities. Information about genetic material was

also available. The PSPs cover an area of c. 170,000 ha of E. grandis hybrid planta-

tions (see Fig. 6.1). Some PSPs are located inside thinned stands. As each PSP was

measured more than once, there were 3281 sets of observations. Table 6.1 summa-

rizes the measurements made. Additionally, taper functions were developed based

on diameter measurements along the stem from a set of 401 felled trees.

Linking process-based and empirical models

Both 3-

PG and E-GROW ARCEL can be applied to obtain predictions of growth and

yield under different management practices (establishment, re-establishment or cop-

07Amaro Forests - Chap 06 25/7/03 11:05 am Page 69

69 Linking Process-based and Empirical Models

Table 6.1. Number of measurements of the PSPs used to develop

E-GROW ARCEL.

Age

Dominant height (m)

(years) <15 15–20 20–25 >25 Total

<3 153 203 17 0 373

3–5 183 881 751 117 1932

5–7 2 90 535 329 956

>7 0 0 5 15 20

Total 338 1174 1308 461 3281

pice), genetic material and initial stem density. In this study the link between mod-

els assumed re-establishment as the standard management practice for clonal E.

grandis hybrids with 1111 trees/ha. Under these conditions,

E-GROW ARCEL estimated

MAI

for a range of SI, resulting in a robust relationship, deﬁned by Equation 1.

SI = 10.84 + 0.403  MAI

– 0.001  (MAI

)

(1)

= 0.99 RMSE = 0.26 m

Equation 1 provides the necessary link between predictions of MAI

from 3-PG and

the SI required as an input for

E-GROW ARCEL.

Results

The values of MAI estimated by 3-PG for 6-year-old stands in different regions were

compared with observations made annually in PSPs in ten of 19 regions (Fig. 6.2),

showing the observed MAI for each region. The nine regions without PSP data are

presented in Fig. 6.2, indicating the 3-

PG predictions under different environmental

conditions. The estimated values obtained with 3-

PG assumed the real climate condi-

tions and the applied silvicultural practices such as fertilization, soil preparation

and weed control. The histograms show that 3-

PG provides an accurate estimate of

MAI estimated MAI observed

46 42 28 37 38 42 55 49 35 48 31 60 55 33 43 37 47 4034

MAI (m

/ha/year)

Cachoeirinha

Fábrica

Microbacia

Pastinho

Sede

Serra

Viveiro

Alcobaça

Caravelas

COSB

Joeirana

Lagoinhas

Nova Brasília

Nova Viçosa

Itauninhas

PRF

Queixada

Santana

Sayonara

Fig. 6.2. Mean annual increment (MAI) in different regions planted in 1995, estimated using 3-PG (bars),

and observed MAI (circles) at age 6 years.

07Amaro Forests - Chap 06 25/7/03 11:05 am Page 70

70 A.C. Almeida et al.

the MAI likely to be obtained in any area.

Values of basal area and stand volume at 6 years of age, measured in PSPs and

estimated by 3-

PG, are presented in Table 6.2 for each region.

Figures 6.2 and 6.3 and Table 6.2 show that 3-

PG is well calibrated for age 6-

years. The resulting MAI

value was inserted in Equation 1 generating the SI for

each region that was used in

E-GROW ARCEL, to predict the volume curve of commer-

cial products.

We selected the Nova Viçosa region as an example of the ﬁnal results. 3-

PG esti-

mated a MAI

of 55 m

/ha



year, which generated an SI of 30 m, using Equation 1.

Based on this site index,

E-GROW ARCEL describes the volume curve and the structure

of the stand at each age of the projection period. Figure 6.4 shows the volume curve

by predeﬁned log type based on its small end diameter (SED) and log length. The

distribution of diameter at breast height (DBH) is also obtained. Figure 6.5 presents

the log volume for each DBH class at age 7 years.

Discussion and Conclusions

Long-term planning for the production of fast-growing species is strongly affected

by the productivity of the area concerned. Traditionally, potential productivity is

estimated from growing history and/or local expertise, without considering the eco-

Table 6.2. Basal area and stand volume observed in PSPs and estimated by 3-PG at age 6 years.

Basal area Basal area Stand volume Stand volume

Region observed (m

/ha) estimated (m

/ha) observed (m

/ha) estimated (m

/ha)

Cachoeirinha 21.1 21.2 200.3 203.5

Fabrica 28.0 25.7 296.0 276.6

Microbacia 23.3 24.2 268.2 250.2

Sede 21.3 22.3 245.6 219.9

Viveiro 24.4 24.4 274.4 254.6

Nova Viçosa 26.5 28.7 324.9 331.7

Itauninhas 22.3 21.0 241.3 200.3

PRF 23.6 24.8 258.6 260.8

Santana 26.9 26.1 298.2 282.7

Sayonara 21.5 23.6 245.8 240.2

102030405060

MAI observed (m

/ha/year)

y = 0.99 x – 1.14

= 0.92

Fig. 6.3. Relationship between observed and estimated MAI by 3-PG. The goodness of ﬁt of the regression

line is given by the R

value of 0.92.

MAI estimated (m

/ha/year)

07Amaro Forests - Chap 06 25/7/03 11:05 am Page 71

71 Linking Process-based and Empirical Models

100

150

200

250

300

350

400

/ha)

SED 16 cm SED 7 cm SED 4 cm

Volume (m

2 3 4 5 6 7

Age (years)

Fig. 6.4. Volume curve per predeﬁned log type based on its small end diameter (SED).

/ha)

SED 16 cm SED 7 cm SED 4 cm

Volume (m

5 6 7 8 9 10 11 12 13 1415 1617 18 1920 2122 23 2425 26

DBH distribution (cm)

Fig. 6.5. Diameter at breast height (DBH) distribution and log volume per small end diameter (SED) at age

7 years.

physiological processes involved. This is critical when production in new areas,

where no forest has been planted before, is being planned. Another important aspect

for forestry industries is information about the product volumes likely to become

available from any area. The hybrid approach developed in this study provides

information about potential productivity and the product mix.

This study has illustrated the signiﬁcant variation in MAI that occurs between

egions as a consequence of environmental conditions. The 3-

PG model is a powerful

and practical tool that can be used to analyse and predict these effects, while its

combination with

E-GROW ARCEL provides enough detail in terms of forest products

to meet planning needs.

This approach is being tested in operational practice by Aracruz Celulose S.A.

in Brazil. The r

esults are encouraging and appear likely to lead to continuous

improvements in forest planning and management.

07Amaro Forests - Chap 06 25/7/03 11:05 am Page 72

72 A.C. Almeida et al.

Acknowledgements

We acknowledge with thanks permission given by Aracruz Celulose S.A. to publish

these data and the results of our analyses of them. We also acknowledge our col-

leagues Ricardo Penchel, Sebastião Fonseca and Simone M. Barddal for their efforts

on technical support and database maintenance. Finally we thank Marcelo

Wiecheteck and Natalino Calegario for their review of the manuscript.

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7 A Strategy for Growth and Yield

Research in Pine and Eucalypt

Plantations in Komatiland Forests

in South Africa

Heyns Kotze

Abstract

In Komatiland Forests the objectives of growth and yield research are to develop a range of

empirical stand-level growth and yield models for thinned pine stands. The models are used

for resource description, growth and yield predictions for the purpose of management plan-

ning and for the development of optimum stand-level management regimes.

The growth and yield research programme consists of four main components, namely a

ﬁeld programme, long-term data management, growth modelling and the development of

simulation systems. For each of these components a strategy has been developed. In the ﬁeld,

programme data are collected for each of the target model components from a number of

sources, such as spacing trials, permanent sample plots (PSPs), silvicultural response trials,

plantation inventories and destructive sampling for volume and taper data.

The modelling strategy is to develop multi-component model architectures for modelling

stand-level growth, namely dominant height, unthinned basal area and survival. For thinned

stands, additional functions for the modelling of the basal area thinning ratio and the basal area

response after thinning are required. Depending on the data, both the Chapman–Richards-type

and the Schumacher-type functions are used for modelling unthinned stand-level basal area.

Various methods are used for modelling basal area response after thinning, e.g. the index of

suppression or the age-adjustment method. A major challenge in growth modelling is to

develop models for thinned stands based on PSP data only, while conforming to the hypothesis

of thinned stand growth. Stand structure is modelled using the Weibull function in conjunction

with the method of moments approach for recovering the relevant Weibull parameters.

Finally, the models are built into simulation systems for stand-level scenario analysis, e.g.

the development of rule-based thinning and pruning systems, and also forestry scenario analy-

sis. However, the main function of stand-level growth and yield models is still to provide for

more accurate company planning systems.

Introduction

The Komatiland Forests plantations are situated on the great north-eastern escarp-

ment of South Africa (Fig. 7.1). The company is a recently created subsidiary of the

Komatiland Forests, Research Division, South Africa

Correspondence to: hkotze@safcol.co.za