W O R K I N G P A P E R
MAXIMIZING THE CARRYING CAPACITY OF FOREST ECOSYSTEMS: M O D r n I I J G AND FORMATION O F
THE
MOST PRODUCTIVE STANDS
L. Kairiukstis A. Juodvalkis
October 1986 WP-86-058
I n t e r n a t i o n a l I n s t i t u t e 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 OFTHE
MOST PRODUCTNE SI'ANDSL. K a i r i u k s t i s * A. J u o d v a l k i s * *
O c t o b e r 1986 WP-86-58
*
D e p u t y Leader, E n v i r o n m e n l P r o g r a m I n t e r n a t i o n a l I n s t i t u t e forApplied S y s t e m s A n a l y s i s A-2361 L a x e n b u r g , A u s t r i a
* * L i t h u a n i a n R e s e a r c h I n s t i t u t e of F o r e s t r y , K a u n a s , 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 I n t e r n a t i o n a l I n s t i t u t e 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 n o t n e c e s s a r i l y r e p r e s e n t t h o s e of t h e I n s t i t u t e o r of i t s National Member Organizations.
INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS 2361 L a x e n b u r g , Austria
Foreword
The f o r e s t i s o n e 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 n e c e s s a r y 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 p l a c e f o r human beings. In t h e interaction between t h e sun's e n e r g y and t h e a i r ' s c a r b o n dioxide, trees produce s t o r e d e n e r g y 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 c o l l a b o r a t o r Dr. Antanas Juodvalkis, at IIASA and a t t h e Lithuanian R e s e a r c h Institute of F o r e s t r y r e s p e c t i v e l y , h a v e both had long e x p e r i e n c e in r e s e a r c h and modelling of f o r e s t ecosystems. In t h i s p a p e r t h e y 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 a p p r o a c h i s based o n 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 c r e a t i o n 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 o v e r l a p and s t a n d density i s made for d i f f e r e n t p h a s e s of stand development. The model calculates t h e optimal number of trees in e a c h 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 a l r e a d y r e s u l t e d 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 v a s t investigations (more t h a n 400 permanent experimental plots), t h e t h e o r e t i c a l 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 c o n s t r u c t e d and s t a n d a r d s t o form maximally productive stands were worked out.
The e l a b o r a t e d 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) c r e a t i o n , 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 d i f f e r e n t p h a s e s of stand development are different.
In young stands, ( p r o c e s s of ecosystem c r e a t i o n ) 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) c r e a t i o n , i t was noted t h a t in p r e m a t u r e 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 s t o c k and maximal total stand productivity. This i s achieved in t h e c a s e when t h e crown c l o s u r e i s maximal with a n optimal rate of mutual o v e r l a p and t h e s t a n d i s formed from maximally productive trees distributed at a n optimal distance f r o m o n e a n o t h e r .
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 s t a n d s have been worked out. Such s t a n d a r d s h a v e 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 a c c o r d a n c e with set s t a n d a r d s h a s a l r e a d y resulted in a productivity i n c r e a s e 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 h a s 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 OFTHE
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 i n c r e a s e f o r e s t productivity. In tackling t h i s problem, intermediate cutting i s p a r t i c u l a r l y important. I t is o n e 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 t a k e n 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 s p e c i e s composition, s t r u c t u r e and productivity, i.e., h e must have a simulation model which provide a n insight into t h e p r o b a b l e s t a n d development. In p r a c t i c e , h e must deal with p r o t o t y p e s o r s t a n d a r d s 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 s t a n d a r d s and programs must b e differentiated according t o s p e c i e s 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 t a s k w a s to:
elucidate t h e r e g u l a r i t i e s of n a t u r a l and a r t i f i c i a l 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 s t a n d a r d s 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 s t a n d s in f o r e s t r y p r a c t i c e p a r t i c u l a r l y by means of thinning.
On t h e basis of t h e a b o v e , w e constructed a simulation model, calculated t h e s t a n d a r d s 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 Organiza- tions) World Congress held in Ljubljana, Yugoslavia (September 7-21, 1986).
*Deputy Leader: Environment Program, International Institute f o r 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
CONSTRUCTIONData from more t h a n 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 t e m p o r a r y experimental plots w e r e a l s o used. The s t a n d s included different s p e c i e s composition, s t r u c t u r e and a g e . The investigations r e s u l t e d 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 i n t e r n a l 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 e f f e c t of intermediate cutting on tree growth and stand productivity.To a s c e r t a i n t h e c o r r e l a t i o n between s e p a r a t e assessment indices, more t h a n 300 d i f f e r e n t equations were derived.
I t w a s found t h a t n a t u r a l s t a n d s do not a t t a i n maximally possible productivity because 40-60% of t h e trees a r e of lower o r low productivity. The p r o c e s s e s of self-regulation in s t a n d s o c c u r through intense competition between t h e individual trees. This r e s u l t s in wasted e n e r g y and, consequently, in r e t a r d a t i o n of f o r e s t growth. Thus, a r t i f i c i a l 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 r e v e a l e d 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 e n e r g y r e c e i v e d 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 e n e r g y i s r e c e i v e d in t h e s t a n d s (see Figure 1).
Second: effectiveness of t h e s o l a r e n e r g y 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 u s e of s o l a r radiation obtained by t h e crowns of variously developed trees i s not equal. The h i g h e r t h e tree productivity in annual increment p e r stand volume in m3 a n d t h e more productive t h e i r needles o r l e a v e s in annual increment p e r leaves weight in tons, t h e h i g h e r t h e production of wood increment p e r unit of a b s o r b e d e n e r g y . The coefficient of profitable s o l a r e n e r g y use f o r both t h e Physiologically Active Radiation (PhAR) a n d 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 p e r c e n t a g e of more productive trees. Class A trees are a b l e , a f t e r thinning, with least e x p e n d i t u r e of substance and e n e r g y , t o produce a much more and b e t t e r quality wood. This produces a positive influence on t h e o v e r a l l productivity of s t a n d s (Figure 2).Finally: s t a n d 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 s t a n d 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 r a d i a t i o n , depending upon t h e s u r f a c e d e p t h of s p r u c e s t a n d ; in t h e t o t a l s o l a r r a d i a t i o n case: at f a i r
2 2
w e a t h e r = 1.1-1.2 cal/cm min; at dull w e a t h e r
=
0.4 cal/cm min.D u b r a v a Experimental F o r e s t , Kaunas Region, Lithuanian SSR, USSR.
C u r r e n t l y , many d i f f e r e n t methods are a v a i l a b l e t o d e t e r m i n e t h e optimal s t a n d d e n s i t y , among which i t i s f e a s i b l e t o single o u t t h r e e major t r e n d s :
a ) t h e optimal s t a n d density i s e s t a b l i s h e d o n t h e basis of investigations of growth p r o c e s s e s of s t a n d with d i f f e r e n t initial density (Timofejev, 1957;
Kondratiev, 1959; Wiksten, 1965; Majorov, 1968; Kazimirov, 1972; a n d 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 b a s i s 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; S t a h e l i n , 1949;
Geworkiantz, 1947; Becking, 1954; K r a m e r , 1966; Thomasius, 1978; a n d o t h e r s ) .
c ) t h e optimal s t a n d density i s determined on t h e b a s i s of t h e d e p e n d e n c e of t h e annual increment magnitude on s t o c k density (Assman, 1961; Matuzanis et al., 1966; Z a g r e j e v , 1962; Kozhevnikov, 1971, a n d o t h e r s ) .
W e h a v e verified a v a s t number of methods a n d 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 c o n s t r u c t i o n of dynamic models of maximally p r o d u c t i v e s t a n d s . W e c a r r i e d o u t silvicultural/physiological investigations on t h e productivity of s t a n d s 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 s t a n d 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 s t o c k
@
Productivity according t o the Ieaveslneedles Productivity according t o the volume@
" i j b n g a b l e classes including changesFigure 2. P r o d u c t i v i t y of trees of d i f f e r e n t development classes a n d i t s v a r i o u s s t a g e s d u r i n g t h e t r a n s i t i o n s
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 a t t h e conclusion t h a t density optimization must b e b a s e d on crown p a r a m e t e r s of maximally p r o d u c t i v e trees ( c l a s s 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 s p a n . In s u c h optimal s p a c e t h e h i g h e s t annual increment of s t o c k 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 r e f l e c t i n g t h e development a n d p r o d u c t i v i t y level of a tree a n d i t s state in s p a c e (canopy).
Second, as previously d e t e r m i n e d , 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 p r o j e c t i o n area i s c o n s i d e r a b l y 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 s t a n d density optimization.Thus, we c a n 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 s t a n d d e n s i t y t o b e determined f o r t h e e n t i r e p e r i o d of s t a n d growth.
W e h a v e investigated growth c h a r a c t e r i s t i c s a n d 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 d i s c o v e r e d a new phenomenon, t h e so- called s t r e s s eflect which o c c u r s d u r i n g 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 d i s c o v e r e d f i x e d limits of t h e c r i t i c a l a p p r o a c h of crowns a t which trees e n t e r into a n intra-specific competitive i n t e r r e l a t i o n s h i p , r e s u l t i n g 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:
w h e r e
x
=
h e i g h t 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 d u r i n g t h e s u b s e q u e n t a p p r o a c h of crown, t h e mutual s u p p r e s s i o n of trees d e c r e a s e d while a n n u a l growth increment i n c r e a s e d (Figure 3).
F i g u r e 3. Generalized scheme of origin a n d formation of f o r e s t ecosystem.
Taking i n t o c o n s i d e r a t i o n t h e a b o v e phenomenon, t h e optimal density c r i t e r i o n c a n n o t b e identical d u r i n g t h e whole p e r i o d of s t a n d growth e v e n when t h e a i m i s t h e kame--to grow maximally p r o d u c t i v e s t a n d s .
S t r i v i n g f o r significant growing s t o c k increment in a young s t a n d i s senseless.
In young s t a n d s , maximal growing s t o c k involves c o n s i d e r a b l e growth r e t a r d a t i o n of individual trees. Consequently, s t a n d productivity a n d stability d e c r e a s e a n d t h e s t a n d s m a t u r e l a t e r . Thus, in young s t a n d s , 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 c o n s i d e r e d such t h a t i t eliminates intra-specific competition, e n s u r e s maximal h e i g h t and d i a m e t e r 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 c o n t r i b u t e s t o t h e t o t a l productivity during felling r o t a t i o n and t o speeding up t h e maturity p r o c e s s . During t h i s period, t h e optimal s t a n d 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. I t i s established according t o t h e following formula:
where
Ngpt
=
optimal number of t r e e s / h a ;Q
=
maximum possible crown c o v e r a r e a during crown c l o s u r e , m2/ha;S
=
crown and r o o t s p a c e f o r o n e tree (m2) a t t h e c r i t i c a l distance between crowns.Following t h e effect of. stress and ecosystem c r e a t i o n , t h e optimal density in f o r e s t s t a n d s i s t h a t which provides maximal annual increment of t h e growing stock and maximum t o t a l 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 r e v e a l e d t h a t s t a n d s meet such requirements when t h e following t h r e e conditions are combined in them:
a ) crown c o v e r i s maximized;
b) 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 o n e a n o t h e r .
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 i s obtained i n the case where the ecosystem u t i l i z e s the space maximally, i.e., i n t h e case w h e r e t h e a r e a of the c r o w n cover i s maximal. The investigations show t h a t n a t u r a l s t a n d s , r e g a r d l e s s of t h e i r s p e c i e s composition and a g e , do not a t t a i n potentially possible crown c l o s u r e and d o not e n t i r e l y utilize t h e whole complex of soil/light conditions. T h e r e f o r e , they do not give t h e i r potentially possible productivity. The fact i s , 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 s p e c i e s 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 l a b o r a t o r y . 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 s p e c i e s 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, 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 o n l y w h e n possible c r o w n cover a r e a i s c h i e f l y covered b y c r o w n s of m a x i m a l l y p r o d u c t i v e trees, i . e . , t r e e s w i t h the most p r o d u c t i v e 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 c l a s s e s 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 i t s horizontal projection a r e a . W e have a s c e r t a i n e d 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). T h e r e f o r e , 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 c l a s s e s of t r e e s ) .
The investigations and t h e o r e t i c a l calculations have indicated t h a t when a stand consists of well-developed t r e e s , and depending upon s p e c i e s and a g e , i t s productivity is by 5-25% h i g h e r t h a n t h e annual increment of n a t u r a l s t a n d s 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 a c h i e v e d w h e n t h e c r o w n s a r e s i t u a t e d a t an o p t i m a l d i s t a n c e from one a n o t h e r w i t h o p t i m a l 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 e x p r e s s e d through crown p a r a m e t e r s . The e x t e n t of crown o v e r l a p must b e allowed for. T h e r e f o r e , in t h e proposed method of stand density determination, t h e indices of t h e d i s t a n c e among trees may b e r e p l a c e d by t h o s e of crown diameter and t h e e x t e n t of t h e optimal crown overlap.
The optimal crown o v e r l a p 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 e x t e n t of crown o v e r l a p (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 e x t e n t of t h e i r crown o v e r l a p . W e have explained t h a t within a stand t h e optimal crown o v e r l a p 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 ( c l a s s A).
Percent of crown overlap
Figure 5. Dependency of annual increment of tree (1) and s t a n d (2) b a s a l 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 h e l p of t h e following formula:
w h e r e
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
=
optimal area of horizontal crown p r o j e c t i o n of well-developed t r e e s , m2;Popt
=
e x t e n t of optimal crown o v e r l a p , 2.While establishing t h e optimal density a n d c o n s t r u c t i n g t h e models of maximally p r o d u c t i v e one-storied s t a n d s , g r e a t a t t e n t i o n 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 s t a n d s , t h e optimal growth conditions f o r trees of t h e most valuable s p e c i e s w a s a l s o ensured. The t o t a l productivity of mixed s t a n d s 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 c o r r e l a t i o n between t h e single assessment indices of a tree and a s t a n d as well as t h e method of s t a n d 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 s p e c i e s 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. The values of t h e p a r a m e t e r s are:
A
=
a g e , y e a r ;S
=
section area in ha;Qplot
=
area of t h e l a y e r projection in t h e section, in m 2 ; Q=
a r e a of t h e l a y e r projection in m 2 /ha;q
=
area of crown projection of a n individual tree without overlapping, in m 2 ;2
qp
=
crown projection area of a n individual tree in m ; 2qwt
=
crown a r e a of t h e optimal projection in m ; q,=
mean area of a crown projection in m2;N
=
number of trees in t h e area unit;Zg
=
increment of stand basal area of a se arate tree in m2;Zc
=
increment of a stand basal a r e a , in m /ha;F
d
=
diameter of a tree in cm;dgpt
=
optimal diameter of a tree in cm;Z,
=
r a d i a l increment during a one y e a r period in cm;P
=
p e r c e n t of t h e overlapping crown;T
=
index of a f o r e s t type;=
index of a tree species;h
=
height of a tree in m;h w t
=
optimal height of a tree in m;GA
=
optimal sum of stand basal area in m2/ha;Nwt
=
optimal number of trees in ha;MA
=
optimal volume of a stand, in m3/ha;F
=
optimal form index; and a=
equation p a r a m e t e r s .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 u s e experimental plots in t h e m o s t dense s t a n d s in t h e whole r a n g e indicated in t h e c o n s t r a i n t s 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 p r e s e n t e d s e p a r a t e l y f o r e a c h tree. These measurements are n e c e s s a r y t o determine t h e a r e a of inevitable glades in t h e stand and t o c a l c u l a t e t h e optimal crown overlap. If t h e stand contains "windows" ( o r s q u a r e s ) , i.e., a r e a s which are g r e a t e r t h a n 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 p r o j e c t i o n areas without overlapping.
In o r d e r t o d e t e r m i n e 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 p r o d u c i n g t h e maximum wood i n c r e m e n t in t h e area unit is c o n s i d e r e d 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 i n t e r v a l , 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 a n d 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 d i s t a n c e i s e s t a b l i s h e d in t e r m s of t h e optimal crown p a r a m e t e r s a n d t h e p e r c e n t of optimal crown o v e r l a p . 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 s t a n d b a s e area a n d volume a f f e c t i n g t h e maximum wood increment are o b t a i n e d 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
MAXIMALLY
PRODUCTIVE STANDS AND THEIR APPLICATIONBased 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 p r o d u c t i v e 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 s p e c i e s ' 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 i n d i c e s of s t a n d s i n 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 a n y a g e .
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 s o l v e s 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 p r o d u c t i v e s t a n d s . The point i s , 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 a n d 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 c a l c u l a t e d s t a n d a r d s must b e formed a r t i f i c i a l l y by i n t e r m e d i a t e cutting. Thus, a f o r e s t e r n e e d s 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 s t a n d s . 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 d e t a i l 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 a n d p r o d u c t i v i t y o c c u r r i n g u n d e r t h e influence of i n t e r m e d i a t e 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 m o r e t h a n 3 0 0 p e r m a n e n t e x p e r i m e n t a l p l o t s in which i n t e r m e d i a t e c u t t i n g of d i f f e r e n t density was a p p l i e d 2-6 times. This allowed u s t o d e t e r m i n e 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 d e p e n d e n c e of t h e s i z e of t h e annual t i m b e r volume increment on t h e e x t e n t of thinning, t h e optimal a n d 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 a n d t h e optimal regime of i n t e r m e d i a t e 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 e s t a b l i s h e d (Kairiukstis a n d Juodvalkis, 1985). An example f o r s p r u c e ( P i c e a a b i e s , K a r s t e n ) i s given in F i g u r e 8.
Hence, p r o g r a m s t o form maximally p r o d u c t i v e 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 p u r p o s e s . The e s s e n c e of t h e p r o g r a m s 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 i n t e r m e d i a t e c u t t i n g , t h e s t a n d a r d s discussed a b o v e i n d i c a t e t h e number of well-developed ( c l a s s A) t r e e s , s t a n d b a s a l a r e a , a n d t i m b e r 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 a c c o r d i n g 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 a p p l i c a t i o n s of i n t e r m e d i a t e cutting.
Table 1. 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 d i f f e r e n t s p e c i e s depending upon t h e mean height (m) of well- developed t r e e s when opening of stands and c l e a r i n g s are r e p e a t e d e v e r y f i v e y e a r s while thinning and intermediate cutting e v e r y t e n y e a r s .
Height Oak Ash S p r u c e Aspen Birch
of well- (Quercus (Fraxinus ( a c e a (PopuLus (Betula
developed r o b u r ) ezceLsior) a b i e s K a r ) t r e m u l a ) v e r r u c o s a )
trees stands stands stands s t a n d s stands
5 10 15 20 25 30 Stand basal area (rn2/ha)
Figure 7. Homeostatic abilities and thinning e f f e c t (30 year-old s p r u c e stand).
horizontal dashed line
- - - =
reduction of stand basal area by thinning;convex c u r v e s
- =
e x t e n t and duration e f f e c t s of thinning.The s t a n d a r d s are assigned not only f o r c a r r y i n g out intermediate cutting but a l s o 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 l e f t 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 s t a n d a r d s 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 b e k e p t are e x p r e s s e d depending upon t h e mean height of well- developed trees. A generalized s t a n d a r d f o r f o r e s t t y p e s of similar productivity c a n thus b e applied.
In t h e p r o c e s s of s t a n d a r d 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 s t a n d 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 s t a n d 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. H e r e t h e mean height of trees and t h e i r t o t a l number are compared with t h e standard.
Cutting i s applied on t h e allocated areas in young s t a n d s 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 s t a n d depending upon age.
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