Maximizing the Carrying Capacity
of Forest Ecosystems: Modelling
and Formation of the Most
Productive Stands
Kairiukstis, L. and Juodvalkis, A.
IIASA Working Paper
WP-86-058
October 1986
Kairiukstis, L. and Juodvalkis, A. (1986) Maximizing the Carrying Capacity of Forest Ecosystems: Modelling and Formation
of the Most Productive Stands. IIASA Working Paper. IIASA, Laxenburg, Austria, WP-86-058 Copyright © 1986 by the
author(s). http://pure.iiasa.ac.at/2802/
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WORKING PAPER
MAXIMIZING THE CARRYING CAPACITY OF FOREST
ECOSYSTEMS: M O D r n I I J G AND FORMATION OF THE
MOST PRODUCTIVE STANDS
L. Kairiukstis
A. Juodvalkis
October 1986
WP-86-058
International Institute
for Applied Systems Analysis
NOT FOR QUOTATION
WITHOUT THE PERMISSION
OF THE AUTHORS
K A X I M I m G THE CARRYING CAPACITY OF M)REST
ECOSYSTEMS: MODELUNG AND MlRKATION OF
THE MOST PRODUCTNE SI'ANDS
L. K a i r i u k s t i s *
A. Juodvalkis**
October 1986
WP-86-58
* D e p u t y Leader, E n v i r o n m e n l Program
I n t e r n a t i o n a l I n s t i t u t e for
Applied S y s t e m s A n a l y s i s
A-2361 Laxenburg, A u s t r i a
* * L i t h u a n i a n Research I n s t i t u t e of
Forestry, Kaunas, G i r i o n y s
L i t h u a n i a n SSR, USSR
Working P a p e r s a r e interim r e p o r t s o n work of t h e International
Institute f o r Applied Systems Analysis a n d h a v e r e c e i v e d only limited
review. Views o r o p i ~ i o n s e x p r e s s e d h e r e i n cio not necessarily
r e p r e s e n t t h o s e of t h e Institute o r of i t s National Member
Organizations.
INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS
2361 Laxenburg, Austria
Foreword
The f o r e s t i s one of t h e most important r e s o u r c e s of t h e biosphere. T r e e s are
necessary components of t h e ecological p r o c e s s t h a t t h e e a r t h a possible dwelling
place f o r human beings. In t h e interaction between t h e sun's energy and t h e a i r ' s
carbon dioxide, trees produce s t o r e d energy and oxygen, and t h e root systems
bind t h e soil p a r t i c l e s and r a i s e t h e soil's productive capacity. From a n economic
point of view, trees a r e r a w material f o r fuel, lumber, t h e chemical industry,
modern medicines, etc. However, t h e r e are r e p o r t s in t h e p r e s s almost daily about
forest decline. Hence, t h e forest needs much m o r e attention needs to b e given to
ways of improving f o r e s t management systems and increasing t h e c a r r y i n g capacity
of t h e f o r e s t itself.
Academician Leonardas Kairiukstis and his collaborator Dr. Antanas
Juodvalkis, at IIASA and a t t h e Lithuanian Research Institute of F o r e s t r y
respectively, have both had long experience in r e s e a r c h and modelling of f o r e s t
ecosystems. In this p a p e r they p r e s e n t interesting new a p p r o a c h e s to modelling
and t h e formation of a forest ecosystem of maximal productivity. Their approach
i s based on t h e effective utilization of s o l a r energy and "stress"phenomenon which
o c c u r s during t h e creation of t h e f o r e s t ecosystem.
An optimization of crown p a r a m e t e r s , t h e i r overlap and stand density i s made
for different phases of stand development. The model calculates t h e optimal
number of trees in each time span (standard stands) which would enable an
i n c r e a s e in c a r r y i n g capacity of t h e f o r e s t ecosystem. An application of t h e s e
s t a n d a r d s in t h e thinning p r a c t i c e of t h e Lithuanian SSR h a s already resulted in a
productivity i n c r e a s e of forest stands.
P r o f e s s o r R.E. Munn
Leader, Environment Program
International Institute f o r
Applied Systems Analysis
A-2361 Laxenburg, Austria
summary
On t h e basis of long-term (over 30 y e a r s ) and vast investigations (more than
400 permanent experimental plots), t h e theoretical basis f o r c r e a t i n g a maximally
productive f o r e s t was developed and new methods t o determine optimal density
were suggested. Also, models t o simulate stands of maximal productivity were
constructed and standards t o form maximally productive stands were worked out.
The elaborated methods of density optimization are based on a s e a r c h f o r t h e
optimal crown p a r a m e t e r s and optimal growing s p a c e ensuring maximal increment
of t h e whole stands. On t h e basis of a newly-revealed phenomenon, t h e so-called
s t r e s s effect which o c c u r s during t h e p r o c e s s of ecosystem (biocenoses) creation,
i t w a s found t h a t t h e c r i t e r i a of optimal stand density in different phases of stand
development are different.
In young stands, (process of ecosystem creation) t h e optimal density is t h a t
density which eliminates t h e mutual influence (competition) of t h e trees and
e n s u r e s maximum height increment f o r a possibly g r e a t e r number of trees.
Following ecosystem (biocenoses) creation, i t was noted t h a t in premature and
middle-aged stands, t h e optimal density i s such t h a t i t provides t h e maximum annual
increment of t h e growing stock and maximal total stand productivity. This i s
achieved in t h e c a s e when t h e crown closure i s maximal with a n optimal rate of
mutual overlap and t h e stand i s formed from maximally productive trees
distributed at a n optimal distance f r o m one another.
Based on t h e above, t h e s t a n d a r d s of maximally productive f o r e s t stands have
been worked out. Such standards have been widely implemented in exploitive
f o r e s t s in t h e Lithuanian SSR as well as in western and north-western regions of
t h e USSR. Specialized f o r e s t growth undertaken in accordance with set standards
has already resulted in a productivity increase of up t o 15-20%. The utilization of
wood p e r unit area h a s been significantly augmented and t h e cutting cycle of
stands has ben noted t o b e much s h o r t e r .
MAXIMIZING THE CARRYING CAPACITY OF FOREST
ECOSYSTEMS: MODELLING A.NI) FORMATION OF
THE MOST PRODUCTIVE STAND*
L. Kairiukstis* a n d A. JuodvaLkis**
1. INTRODUCTION
One of t h e main t a s k s f o r f o r e s t management is t o increase f o r e s t
productivity. In tackling t h i s problem, intermediate cutting i s particularly
important. I t is one of t h e most effective means t o e n s u r e qualitative stands are
obtained. However, i t must b e taken into account t h a t positive r e s u l t s are
achieved when efficient and qualitative thinning is applied and when t h e whole
system of maximally productive stand formation i s scientifically sound. Thus, a
f o r e s t e r must know which, and how, stands must b e formed according t o species
composition, s t r u c t u r e and productivity, i.e., he must have a simulation model
which provide a n insight into t h e probable stand development. In p r a c t i c e , he must
deal with prototypes o r standards of a maximally productive f o r e s t and have
c o n c r e t e programs f o r forming such a f o r e s t . Such standards and programs must
be differentiated according t o species composition of stands, ecological and
geographical regions as well as t o s i t e conditions.
W e have, t h e r e f o r e , studied t h e biological grounds of forming a maximally
productive f o r e s t in more detail. Our task w a s to:
elucidate t h e regularities of n a t u r a l and artificial stand formation;
develop t h e principles and methods f o r constructing simulation models of
maximally productive stands;
e l a b o r a t e standards f o r growing of stands of maximal productivity;
e l a b o r a t e purposeful programs f o r forming such stands in f o r e s t r y p r a c t i c e
particularly by means of thinning.
On t h e basis of t h e above, w e constructed a simulation model, calculated t h e
standards and developed t h e programs t o form maximally productive stands.
$This paper was presented a t the 18th IUFRO (International Union of Forestry Research Organizations) World Congress held in Ljubljana, Yugoslavia (September 7-21, 1986).
*Deputy Leader: Environment Program, International Institute for Applied Systems Analysis,
A-2361 Laxenburg, Austria
**Lithuanian Research Institute of Forestry, Kaunas, Cirionys; Lithuanian SSR, USSR
2. EXPERIMENTAL AND THEORETICAL BACKGROUND FOR
THE MODEL CONSTRUCTION
Data from more than 400 permanent experimental plots of 5-30 y e a r s
duration were used (Kairiukstis, 1977). The trees were mapped and measured.
Intermediate cutting on permanent experimental plots w a s applied 2-6 times. Data
from 80 temporary experimental plots w e r e also used. The stands included
different s p e c i e s composition, s t r u c t u r e and age. The investigations resulted in
establishing t h e following:
-
major r e g u l a r i t i e s of growth and formation of stands;
impact of internal and e x t e r n a l f a c t o r s on t h e magnitude of t h e annual
increment of a tree and stand; and
t h e effect of intermediate cutting on tree growth and stand productivity.
To a s c e r t a i n t h e correlation between s e p a r a t e assessment indices, more than
300 different equations were derived.
I t w a s found t h a t n a t u r a l stands do not attain maximally possible productivity
because 40-60% of t h e trees a r e of lower o r low productivity. The processes of
self-regulation in stands o c c u r through intense competition between t h e individual
trees. This r e s u l t s in wasted energy and, consequently, in r e t a r d a t i o n of f o r e s t
growth. Thus, artificial regulation of stand density and s t r u c t u r e a t a n optimal
level i s t h e essential f a c t o r ensuring i n c r e a s e in stand productivity. The
investigations revealed t h a t stand productivity on comparatively f e r t i l e soils i s
determined by t h e following conditions:
First: quantity and quality o f . s o l a r energy received in t h e stand. This
depends v e r y much upon t h e canopy s u r f a c e and i t s depth being regulated
through t h e thinning systems. The g r e a t e r t h e dips in t h e s u r f a c e of t h e
canopy, t h e lesser t h e albedo, and t h e more s o l a r energy i s received in t h e
stands (see Figure 1).
Second: effectiveness of t h e s o l a r energy utilization by trees and s t o r e y s
and by t h e tree quality and productivity itself. The efficiency of t h e use of
s o l a r radiation obtained by t h e crowns of variously developed trees i s not
equal. The higher t h e tree productivity in annual increment p e r stand volume
in m3 and t h e more productive t h e i r needles o r leaves in annual increment p e r
leaves weight in tons, t h e higher t h e production of wood increment p e r unit of
absorbed energy. The coefficient of profitable s o l a r energy use f o r both t h e
Physiologically Active Radiation (PhAR) and t o t a l S o l a r Radiation (SR) i s
assumed f o r class A* trees = 1.0, f o r trees of class B = 0.8-0.7 and f o r trees
of c l a s s C = 0.7-0.5 respectively. The stand formation by thinning cuttings
enable one t o change t h e composition of t r e e classes and t o i n c r e a s e t h e
percentage of more productive trees. Class A trees are able, a f t e r thinning,
with least expenditure of substance and energy, t o produce a much more and
b e t t e r quality wood. This produces a positive influence on t h e overall
productivity of stands (Figure 2).
Finally: stand productivity i s determined by t h e optimal number of trees p e r
area unit. Due t o t h e f a c t t h a t g r e a t attention i s given t o t h e optimal stand
density in f o r e s t r y l i t e r a t u r e , w e shall discuss t h i s question in more detail.
*The c l a s s i f i c a t i o n of t r e e s w a s e s t a b l i s h e d by L. K a i r i u k s t i s (1969).
Fair weather
Cover
Surface
Average
Depth
Fair weather
Dull weather
Fair weather
Dull weather
. g u r e 1. Albedo (in p e r c e n t ) from t o t a l s o l a r radiation, depending upon t h e
s u r f a c e d e p t h of s p r u c e stand; in t h e t o t a l s o l a r radiation case: at f a i r
w e a t h e r = 1.1-1.2 cal/cm2 min; at dull weather = 0.4 cal/cm 2 min.
Dubrava Experimental F o r e s t , Kaunas Region, Lithuanian SSR, USSR.
Currently, many d i f f e r e n t methods are available t o determine t h e optimal
stand density, among which i t i s feasible t o single o u t t h r e e major t r e n d s :
a)
t h e optimal stand density i s established on t h e basis of investigations of
growth p r o c e s s e s of stand with d i f f e r e n t initial density (Timofejev, 1957;
Kondratiev, 1959; Wiksten, 1965; Majorov, 1968; Kazimirov, 1972; and o t h e r s ) ;
b)
t h e optimal density i s a s c e r t a i n e d on t h e basis of t h e c o r r e l a t i o n between t h e
indices c h a r a c t e r i z i n g t h e density of s t a n d s with d i f f e r e n t assessment indices
of trees (Shustov, 1933; Reinecke, 1933; Wilson, 1946; Stahelin, 1949;
Geworkiantz, 1947; Becking, 1954; Kramer, 1966; Thomasius, 1978; a n d
others).
t h e optimal stand density i s determined on t h e b a s i s of t h e dependence of t h e
annual increment magnitude on s t o c k density (Assman, 1961; Matuzanis et al.,
1966; Zagrejev, 1962; Kozhevnikov, 1971, and o t h e r s ) .
c)
W e h a v e verified a v a s t number of methods and h a v e noted t h a t most of them
are f a r from p e r f e c t f o r t h e construction of dynamic models of maximally
productive stands. W e c a r r i e d o u t silvicultural/physiologicalinvestigations on t h e
productivity of stands and class s t r u c t u r e of trees in s t o r e y s (Kairiukstis, 1973).
W e find t h a t t h e stand density r e f l e c t s tree growth conditions b e t t e r t h a n t h e stock
@
@
Figure 2.
Productivity according t o the Ieaveslneedles
Productivity according t o the volume
" i j b n g a b l e classes
including changes
Productivity of trees of d i f f e r e n t development classes and i t s various
s t a g e s during t h e transitions 2 t o o t h e r c l a s s e s (in % from t h e
productivity of c l a s s A).
density. W e a r r i v e d at t h e conclusion t h a t density optimization must b e based on
crown p a r a m e t e r s of maximally productive trees (class A), on t h e optimum dynamic
s p a c e f o r e a c h tree in e a c h time span. In such optimal s p a c e t h e highest annual
increment of stock growth c a n b e e n s u r e d . With r e g a r d t o t h e crown, t h e following
must b e mentioned. F i r s t , t h e crown i s a sensitive index simultaneously reflecting
t h e development and productivity level of a tree and i t s state in s p a c e (canopy).
Second, as previously determined, t h e c o r r e l a t i o n of t h e magnitude of annual tree
increment with horizontal crown projection area i s considerably c l o s e r ( r = 0.75)
t h a n with growing s p a c e ( r = 0.47). T h e r e f o r e , t h e crown was s e l e c t e d as t h e main
c r i t e r i o n of stand density optimization.
Thus, we can i n f e r t h a t t h e s e a r c h of t h e optimal crown p a r a m e t e r s and
optimal s p a c e rates f o r e a c h a g e c l a s s will e n a b l e t h e optimal stand density t o b e
determined f o r t h e e n t i r e p e r i o d of stand growth.
W e have investigated growth c h a r a c t e r i s t i c s and formation of s t a n d s in
v a r i o u s p h a s e s of t h e i r development. W e discovered a new phenomenon, t h e socalled s t r e s s eflect which o c c u r s during t h e p r o c e s s of c r e a t i o n of f o r e s t
ecosystems (Kairiukstis a n d Juodvalkis, 1975). We a l s o discovered fixed limits of
t h e c r i t i c a l a p p r o a c h of crowns at which trees e n t e r into a n intra-specific
competitive interrelationship, resulting in a high increment d e c r e a s e i r r e s p e c t i v e
of soil o r climatic conditions. The limit of c r i t i c a l a p p r o a c h e s of crown may b e
e x p r e s s e d as follows:
where
x = height of t r e e , in meters (0.5-5.0).
F u r t h e r , i t was found t h a t following t h e c r i t i c a l limit a n d ecosystem c r e a t i o n
during t h e subsequent a p p r o a c h of crown, t h e mutual suppression of trees
d e c r e a s e d while annual growth increment i n c r e a s e d (Figure 3).
Figure 3.
Generalized scheme of origin and formation of f o r e s t ecosystem.
Taking into consideration t h e a b o v e phenomenon, t h e optimal density c r i t e r i o n
cannot b e identical during t h e whole period of stand growth even when t h e a i m i s
t h e kame--to grow maximally productive stands.
Striving f o r significant growing stock increment in a young stand i s senseless.
In young stands, maximal growing s t o c k involves considerable growth r e t a r d a t i o n
of individual trees. Consequently, stand productivity and stability d e c r e a s e and
t h e s t a n d s mature l a t e r . Thus, in young stands, b e f o r e t h e stress e f f e c t o c c u r s ,
t h e optimal density must b e considered such t h a t i t eliminates intra-specific
competition, e n s u r e s maximal height and diameter increment f o r t h e g r e a t e s t
possible number of t r e e s . Also, d u e t o such a n optimal density, t h e culmination of
maximal productivity o c c u r s later and contributes t o t h e t o t a l productivity during
felling rotation and t o speeding up t h e maturity process. During t h i s period, t h e
optimal stand density is determined by crown p a r a m e t e r s of well-developed trees
and t h e c r i t i c a l distance among crowns. It i s established according t o t h e
following formula:
where
Ngpt = optimal number of t r e e s / h a ;
= maximum possible crown c o v e r a r e a during crown closure, m2/ha;
Q
= crown and r o o t s p a c e f o r one tree (m2) a t t h e c r i t i c a l distance between
S
crowns.
Following t h e effect of. stress and ecosystem creation, t h e optimal density in
f o r e s t stands i s t h a t which provides maximal annual increment of t h e growing stock
and maximum total stand productivity. Such density also provides t h e g r e a t e s t
timber volume by t h e a g e of final felling.
Our investigations revealed t h a t stands meet such requirements when t h e
following t h r e e conditions are combined in them:
a)
b)
crown c o v e r i s maximized;
t h e stand consists of maximally productive trees (class A according t o t h e
a u t h o r s , o r class 1.8-11.2 according t o G. Kraft);
c)
maximally productive trees are distributed at a n optimal distance from one
another.
Conforming with t h e first condition, maximal s t a n d p r o d u c t i v i t y is
obtained i n the case where the ecosystem u t i l i z e s the space maximally, i.e., i n
the case where the a r e a of the crown cover is maximal. The investigations show
t h a t n a t u r a l stands, r e g a r d l e s s of t h e i r species composition and a g e , do not attain
potentially possible crown closure and do not entirely utilize t h e whole complex of
soil/light conditions. Therefore, they do not give t h e i r potentially possible
productivity. The fact is, t h a t in any stand t h e r e i s always a c e r t a i n a r e a of
"windows" o r some s m a l l glades where trees might grow. Depending upon t h e
species and a g e , t h e area of such windows in n a t u r a l stands comprises 5-15X of t h e
experimental plot a r e a . These windows are artificially filled with trees while
processing stand d a t a in t h e laboratory. Then t h e a r e a of maximal crown c o v e r
and t h a t of t h e inevitable openings are ascertained. W e have determined t h a t t h e
maximally possible crown c o v e r area depending upon species composition and a g e
comprises 7500-9000 m2/ha, while t h e a r e a of inevitable openings i s 10-25X.
Under t h e second condition, mazimal s t a n d p r o d u c t i v i t y is achieved o n l y
w h e n possible c r o w n cover a r e a is chiefly covered b y crowns of maximally
productive trees, i.e., trees w i t h the most productive crowns-maximal annual
increment of s t e m wood p e r 1 m2 of crown a r e a (Figure 4). Relative crown
productivity of trees of various development classes displays g r e a t diversity.
Within a stand t h e r e i s a p a r t i c u l a r crown a r e a f o r each individual tree in which
t h e highest r e l a t i v e crown productivity i s attained. An optimal a r e a is established
according t o t h e extremum in t h e c u r v e of t h e dependence of r e l a t i v e crown
productivity on its horizontal projection a r e a . W e have ascertained t h a t withing a
stand, t h e optimal a r e a of horizontal crown projection is close t o t h e mean crown
a r e a of well-developed trees (class A). Therefore, f o r p r a c t i c a l purposes, in
o r d e r t o determine t h e optimal horizontal crown projection a r e a , i t i s enough t o
establish t h e mean crown a r e a of well-developed t r e e s .
Horizontal crown projection area (rn2)
Figure 4.
Dependence of r e l a t i v e crown productivity on i t s size (22 year-old
oak stand; A', A, B and C classes of t r e e s ) .
The investigations and theoretical calculations have indicated t h a t when a
stand consists of well-developed t r e e s , and depending upon species and age, i t s
productivity is by 5-25% higher than t h e annual increment of natural stands of t h e
s a m e density.
According t o t h e third condition, m a z i m a l s t a n d p r o d u c t i v i t y i s achieved
w h e n the c r o w n s a r e s i t u a t e d a t an optimal d i s t a n c e from one a n o t h e r w i t h
optimal m u t u a l o v e r l a p .
A s e a r c h for t h e b e s t index reflecting t h e distance among trees showed t h a t
t h e c o r r e l a t i o n between t h e magnitude of t h e annual tree increment and t h e
distance among trees i s highest when t h e distance is expressed through crown
parameters. The extent of crown overlap must be allowed for. Therefore, in t h e
proposed method of stand density determination, t h e indices of t h e distance among
trees may be replaced by those of crown diameter and t h e extent of t h e optimal
crown overlap.
The optimal crown overlap i s established according to t h e extremum of t h e
c u r v e of t h e dependence of t h e annual stand increment magnitude on t h e extent of
crown overlap (Figure 5). I t in t u r n , i s determined f r o m t h e d a t a of t h e c u r v e of
t h e dependence in individual trees on t h e extent of t h e i r crown overlap. W e have
explained t h a t within a stand t h e optimal crown overlap i s similar to t h e mean
overlap of crown of well-developed t r e e s . Consequently, f o r p r a c t i c a l purposes,
t h e indices of t h e optimal crown o v e r l a p may b e r e p l a c e d by t h o s e of t h e mean
crown o v e r l a p of well-developed trees (class A).
Percent of crown overlap
Figure 5.
Dependency of annual increment of tree (1) and stand (2) basal area
on t h e e x t e n t of crown o v e r l a p (36 year-old s p r u c e stand).
Consequently, t h e optimal density of middle-age and t h o s e of maturing s t a n d s
i s a s c e r t a i n e d with t h e help of t h e following formula:
where
Nopt
= optimal number of t r e e s , t r e e s / h a ;
Q,,, = maximum possible crown c o v e r a r e a ; m2/ha;
SWt
Popt
= optimal area of horizontal crown projection of well-developed t r e e s ,
m2;
= e x t e n t of optimal crown o v e r l a p , 2.
While establishing t h e optimal density and constructing t h e models of
maximally productive one-storied stands, g r e a t attention was paid to t h e e x t e r n a l
and i n t e r n a l r e l a t i o n s between single s t r u c t u r a l elements of a tree a n d a stand.
For two-storied stands, t h e optimal growth conditions f o r trees of t h e most
valuable species w a s also ensured. The total productivity of mixed stands w a s
considered t o b e negligible.
The stand growth and formation r e g u l a r i t i e s and correlation between t h e
single assessment indices of a tree and a stand as well as t h e method of stand
density determination enable t h e construction of models of maximally productive
stands. The models include p u r e and mixed stands formed f r o m t h e main species of
t h e Lithuanian SSR according t o predominating forest types.
3. BLOCK SCHEME OF THE MODEL
Figure 6 p r e s e n t s a block diagram of t h e algorithm.
p a r a m e t e r s are:
A
S
The values of t h e
= age, y e a r ;
Qplot
= section area in ha;
= area of t h e l a y e r projection in t h e section, in m 2;
Q
q
= area of crown projection of a n individual tree without overlapping,
= a r e a of t h e l a y e r projection in m 2/ha;
2
=
qp
=
qwt
=
q,
N
=
Zg
Zc
d
=
=
=
=
dgpt
Z,
=
h
=
=
=
P
T
hwt
=
=
=
=
Nwt
GA
MA
F
a
=
=
=
in m ;
2
crown projection area of a n individual tree in m ;
crown a r e a of t h e optimal projection in m 2 ;
mean area of a crown projection in m2;
number of trees in t h e area unit;
increment of stand basal area of a se arate tree in m2;
increment of a stand basal a r e a , in m /ha;
diameter of a tree in cm;
optimal diameter of a tree in cm;
r a d i a l increment during a one y e a r period in cm;
p e r c e n t of t h e overlapping crown;
index of a f o r e s t type;
index of a tree species;
height of a tree in m;
optimal height of a tree in m;
optimal sum of stand basal area in m2/ha;
optimal number of trees in ha;
optimal volume of a stand, in m3/ha;
optimal form index; and
equation parameters.
F
The model algorithm consists in determining t h e maximum density of t h e l a y e r ,
calculating t h e area of t h e horizontal projection of t h e optimal crown, determining
t h e optimal overlapping p e r c e n t of t h e optimal crown, and calculating t h e number
of trees of a c e r t a i n age. To determine t h e maximum density of t h e l a y e r (Block 2),
one should use experimental plots in t h e m o s t dense stands in t h e whole r a n g e
indicated in t h e constraints t o draw t h e plan of tree locations and crown
projections. The whole a r e a of crown projection (qp) and area q , e x c e p t when
overlapping, are presented separately f o r e a c h tree. These measurements are
necessary t o determine t h e a r e a of inevitable glades in t h e stand and t o calculate
t h e optimal crown overlap. If t h e stand contains "windows" ( o r squares), i.e.,
a r e a s which are g r e a t e r than t h a t of an a v e r a g e tree crown, a designated quantity
of trees is artificially included in them and t h e i r crown are included in t h e initial
information. The maximum density of t h e l a y e r in 1 h a area i s found by t h e
computer. This i s t h e sum of t h e crown projection areas without overlapping.
In o r d e r t o determine t h e optimal crown p a r a m e t e r s , t h e c o r r e l a t i o n between
Zg and g p at a p a r t i c u l a r a g e i s being sought. The crown producing t h e maximum
wood increment in t h e area unit is considered optimal. Having t h e optimal crown
p a r a m e t e r s f o r a p a r t i c u l a r a g e interval, we find i t s r e l a t i o n with a g e in all t h e
a g e r a n g e s (Blocks 4, 5 and 10).
When t h e maximum l a y e r density and t h e optimal crown area are known, t h e
optimal number of trees in t h e area unit c a n b e found. F o r t h i s p u r p o s e , however,
t h e optimal d i s t a n c e between t h e trees must b e found. In t h e model, t h i s distance i s
established in t e r m s of t h e optimal crown p a r a m e t e r s and t h e p e r c e n t of optimal
crown overlap. The calculation of optimal p e r c e n t a g e of crown o v e r l a p is
d e s c r i b e d in blocks 11-14. As a r e s u l t of t h e calculations, t h e optimal number of
trees, t h e optimal stand b a s e area and volume affecting t h e maximum wood
increment are obtained f o r t h e given t y p e of f o r e s t s a n d tree s p e c i e s ( s e e Block
10).
4.
STANDARDS OF
APPLICATION
MAXIMALLY PRODUCTIVE
STANDS
AND
THEIR
Based on t h e above-mentioned model, t h e s t a n d a r d s of t h e m o s t productive
s t a n d s f o r p u r e s t a n d s a n d main g r o u p s of species' composition a n d s i t e conditions
h a v e b e e n e l a b o r a t e d . These s t a n d a r d s e x p r e s s optimal indices of s t a n d s in
d i f f e r e n t p e r i o d s of t h e i r growth. The s t a n d a r d s r e f l e c t optimum s t a n d density a n d
s t r u c t u r e at any age.
Determination of t h e optimal s t a n d density a n d t h e model c o n s t r u c t e d solves
only t h e f i r s t p a r t of t h e problem, i.e. establishing s t a n d a r d s of t h e most
productive stands. The point is, t h a t in n a t u r e t h e r e are p r a c t i c a l l y n o s t a n d s with
optimal density and s t r u c t u r e . The s t a n d s which m o s t conform with t h e calculated
s t a n d a r d s must b e formed artificially by intermediate cutting. Thus, a f o r e s t e r
needs thinning p r o g r a m s with t h e a i d of which h e is a b l e t o create optimal stands.
F o r t h i s p u r p o s e i t was n e c e s s a r y to known in detail all t h e r e g u l a r i t i e s of c h a n g e
in s t a n d growth and productivity o c c u r r i n g u n d e r t h e influence of intermediate
cutting.
To t a c k l e t h e s e problems, w e used t h e d a t a from more t h a n 300 permanent
experimental plots in which intermediate cutting of d i f f e r e n t density was applied
2-6 times. This allowed u s t o determine t h e following: t h e e x t e n t a n d d u r a t i o n of
tree r e s p o n s e t o thinning, t h e dependence of t h e size of t h e annual timber volume
increment on t h e e x t e n t of thinning, t h e optimal and c r i t i c a l e x t e n t of thinning
(Figure 7). The optimal t e r m s of re-thinning and t h e optimal regime of
intermediate cutting in s t a n d s of d i f f e r e n t s p e c i e s composition, s t r u c t u r e a n d a g e
was established (Kairiukstis a n d Juodvalkis, 1985). An example f o r s p r u c e ( P i c e a
abies, K a r s t e n ) i s given in Figure 8.
Hence, programs t o form maximally productive s t a n d s were e l a b o r a t e d a n d
suggested f o r p r a c t i c a l purposes. The e s s e n c e of t h e programs l i e s in t h e f a c t t h a t
f o r a r e g u l a r r e p e t i t i o n of intermediate cutting, t h e s t a n d a r d s discussed above
indicate t h e number of well-developed (class A) t r e e s , stand basal a r e a , a n d timber
volume t h a t must b e l e f t a f t e r thinning. The number of trees i s a s c e r t a i n e d
according t o t h e conformity of t h e s t a n d with t h e optimal density in t h e middle of
t h e p e r i o d between t h e two applications of intermediate cutting.
Table 1.
Height
of welldeveloped
trees
Number of trees ( t r e e s / h a ) t h a t must b e l e f t a f t e r felling in p u r e stands
of different species depending upon t h e mean height (m) of welldeveloped t r e e s when opening of stands and clearings are repeated
e v e r y five y e a r s while thinning and intermediate cutting e v e r y t e n
years.
Oak
(Quercus
robur)
stands
Ash
(Fraxinus
ezceLsior)
stands
Spruce
(acea
abies Kar)
stands
Aspen
(PopuLus
tremula)
stands
Birch
(Betula
verrucosa)
stands
5
10
15
20
25
30
Stand basal area (rn2/ha)
Figure 7.
Homeostatic abilities and thinning effect (30 year-old s p r u c e stand).
horizontal dashed line
---
convex c u r v e s
- = extent and duration e f f e c t s of
= reduction of stand basal area by
thinning;
thinning.
The standards are assigned not only f o r carrying out intermediate cutting but
also in projecting forest management by computer. The main assessment index in
c a r r y i n g out intermediate cutting i s t h e number of trees t h a t must b e left while
projecting t h e intermediate cutting t h e volume of cutting-timber t h a t i s to b e l e f t
a f t e r felling.
-
In o r d e r t o simplify t h e standards f o r p r a c t i c a l use, t h e assessment indices of
trees t h a t must be k e p t are e x p r e s s e d depending upon t h e mean height of welldeveloped trees. A generalized standard f o r f o r e s t t y p e s of similar productivity
can thus b e applied.
In t h e p r o c e s s of standard f o r e s t formation in p r a c t i c e , t h e assessed indices
of t h e specific stand at a c e r t a i n height are compared with t h e corresponding
indices given by t h e thinning program (Table I). In t h e planning of intermediate
cuttings, t h e volume o r stand basal area in t h e f o r e s t i s compared with t h e
corresponding indices for such calculations.
In selecting trees f o r cutting in typical places where stands are being formed,
areas of 10x10 m o r 10x20 are allocated. Here t h e mean height of trees and t h e i r
total number are compared with t h e standard.
Cutting i s applied on t h e allocated areas in young stands whereas in o l d e r
stands, t h e trees are selected and marked f o r felling. These areas are examples
for c a r r y i n g out cutting o r f o r selecting trees f o r felling in t h e rest of t h e plot.
Age, years
Figure 8.
Optimum 6 time span of re-thinnings (I), maximum thinning effect (2)
optimal intensity of thinning (3) and p e r c e n t of crown widening (4) in
&cadilosum s p r u c e stand depending upon age.
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I-.
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