A Dynamic Model of the Hungarian Forests

NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR

A DYNAMIC MODEL

OF

THE HUNGARIAN FORESIS

Istvdn Vdlyi*

Ferenc L. Tdth**

August 1984 WP-84-63

*Bureau for Systems Analysis, State Office for Technical Development P.O.B. 565, Budapest, H-1374 Hungary

++Computation and Automation Institute of the Hungarian Academy of Sciences. Budapest, a n d IIASA

Working Papers a r e interim reports on work of the International Institute for Applied Systems Analysis arid have received only limited review. Views or opinions expressed herein do not necessarily represent those of t h e Instit.ute or of its National Member 3rganizations.

INTERNATIONAL INSTITUTE FOR APPJJED SYSTEMS ANALYSIS 2361 Laxenburg, Austria

The objective of t h e F o r e s t Sector Project a t IIASA i s t o s t u d y long- t e r m development a l t e r n a t i v e s for t h e forest s e c t o r on a global basis.

The e m p h a s i s in t h e P r o j e c t is on issues of m a j o r r e l e v a n c e t o i n d u s t r i a l a n d g o v e r n m e n t a l policy m a k e r s in different r e g i o n s of t h e world who a r e responsible for f o r e s t r y policy. forest i n d u s t r i a l s t r a t e g y , a n d r e l a t e d t r a d e policies.

The r e s e a r c h p r o g r a m of t h e Project i n c l u d e s a n a g g r e g a t e d analysis of long-term development of i n t e r n a t i o n a l t r a d e in wood pro- d u c t s , a n d t h e r e b y analysis of t h e development of wood r e s o u r c e s , f o r e s t industrial PI-oduction a n d d e m a n d in & E e r e n t world regions. The o t h e r m a i n r e s e a r c h activity is a detailed analysis of t h e f o r e s t sect.or in indivi- dual c o u n t r i e s . R e s e a r c h on t h e s e mutually support,ing topics is ::arried o u t simultaneously in collaboration between IIASA a n d t h e collaborating

institutions of the Project.

This article represents a case study carried o u t by t h e Hungarian collaborating team of scientists. The issue studied in this work is t h e dynamics of t h e forest resources in Hungary.

Markku Kallio Project Leader

Forest Sector Project

This paper details t h e submodel t h a t describes the development of growing stock in t h e Hungarian Forest Sector Model - a case study of IIASA's Forest Sector Project. The model was originally elaborated for t h e Hungarian Biomass Study and concentrates on the relationships between t h e extension of t h e forest area, harvesting policies a n d t h e development of forests.

Special tribute is paid here t o Wolf Dieter Grossmann of IIASA for his methodological help in constructing t h e model. The extent of t h i s help is illustrated by t h e fact t h a t i t was not until Wolf's visit t o Budapest in 1982 t h a t t h e authors first encountered t h e systems dynamics tech- nique. Modeling work was carried out by t h e authors with a heavy reli- ance on t h e advice and data provided by Aladdr Haldsz and Jdzsef GCmesi.

The model has been implemented in DYSMAP on t h e IIASA VAX computer, using t h e X25 link from Budapest.

1. 1NTRODUCTION

2. PLANTING AND HARVESTING POLICIES IN HUNGARY 3. FORMAL MODEL DESCRIPTION

3.1 Growing Stock 3.2 Harvesting

3.3 F o r e s t Area a n d Afforestation Scenarios 4. VALIDATION AND RESULTS

REFERENCES APPENDIX

A DYNAMIC MODEL

OF

THE HUNGARIAN FORESI'S

lstvdn Vdlyi a n d Ferenc L. Tdth

1. INTRODUCTION

In 1981, a r e s e a r c h program coordinated by t h e Hungarian Academy of Sciences under t h e t i t l e "Long-term Perspectives in Utilization of Materials of Biological Origin," or Biomass Study for short, was s t a r t e d . The project constituted t h e n a t u r a l progression from a former study,

"Survey of t h e Agro-ecological Potential of Hungary" and is now nearing completion. The Biomass Study looked a t t h e problem of how, taking i n t o a c c o u n t natural limits (known from t h e Agro-ecological Survey), should production a n d utilization of t h e biomass be s t r u c t u r e d in order t o achieve different strategic targets. In o t h e r words, t h e dynamics of t h e biomass production-transformation-utilization system were t h e focus of t h e investigation, with special attention given t o t h e interactions between h u m a n activities a n d n a t u r a l conditions. The notion of biomass

comprised, in this study. materials of biological origin; t h a t is, t h e whole phytomass

-

including t h e forests

-

a s well as domestic animals, their by-products, both useful and otherwise, and t h e wastes of animal husban- dry and human settlements. An up-to-date account of t h e total biomass stock a n d production in t h e country has been compiled by t h e Hungarian Central Statistics Office, within the framework of this study. For more information on t h e Biomass Study, see Ldng e t ^al. (1904).

The aim of this paper is t o describe a model used in t h e Biomass Study t o predict t h e development of Hungarian forest resources. Accord- ing t o plans of t h e Hungarian collaborating group with IIASA's Forest Sec- tor Project, t h e model will play the same role in t h e Hungarian Forest Sector Model. Therefore, i t can be regarded as a tool for obtaining answers t o t h e questions raised by Bencze et al. (1984). Another aspect of t h e Hungarian Forest Sector Model h a s been studied by T. Bencze; for an account see Bencze (1984).

2. PLANTING AND HARVESI'ING POLICIES IN HUNGARY

During t h e past 35 years the forest area in Hungary has increased considerably. Forests now occupy about 1,690 thousand hectares, or 18%

of t h e territory of t h e country in contrast t o 12% in 1945; growing stock h a s doubled during t h e same period, achieving 250 million m3. Despite t h e dynamic increase in domestic wood consumption, 60% of the needs a r e now m e t by domestic sources.

A significant amount of broadleaved timber is exported by harvest- ing, a t present about 90% of the annual growth. Excepti.orlally large resources have been devoted t o the extension of pine forests, which a r e

now being planted in t h e plains

-

a b r e a k with earlier practice. Owing t o ecological conditions, t h e proportion of pine forest is still very low, and therefore about 90% of domestic needs m u s t be m e t by imports.

Dynamic planting policies have led t o a shift in t h e direction of younger forests. The corresponding harvesting policies were aimed a t moderating this, by building u p reserves and harvesting from different age groups according t o specified proportions. In r e c e n t years, however, t h e a r e a of new plantations h a s substantially decreased. According t o previous proposals (as formulated, for example, in t h e final report of t h e Agro-ecological Survey), in t h e period between 1960 and 2000 t h e forest a r e a was t o be increased by some 280 thousand hectares. However, if we use t h e t r e n d of t h e c u r r e n t five-year plan, only about 130 thousand hec- t a r e s will be added. Therefore, t h e forest a r e a will not expand by t h e 20%

considered desirable by 2000, b u t it probably will some decades l a t e r - depending on f u t u r e planting policies. (The "desirable" forest a r e a is t h a t a r e a not used for o t h e r activities.) In t h e long r u n , t h e a i m of afforestation a n d harvesting policies is t o develop a species s t r u c t u r e t h a t corresponds t o t h e ecological conditions a n d t h a t has a n evenly dis- tributed age range over t h e desirable area. This would mean reaching a n d maintaining a high level of equilibrium. These a r e t h e main features l.hat we intend t o model in providing a tool for checking t h e different long-term afforestation a n d harvesting policies.

Owing to t h e n a t u r e of t h e forest sector, non-linear relationships a n d effects t h a t spread over extended periods a r e of considerable impor- tance. Examples a r e t h e relations between harvesting a n d growth of forests on the one hand, or rotation periods, ranging from 25 t o 130

years, determining t h e effects of planting policies, on t h e other. As a consequence t h e systems dynamics approach seemed most appropriate here. Therefore o u r simulation uses actual values from 1980 as initial conditions, and incorporates various policies, principles, a n d natural relationships t o compute t h e s t a t e for t h e next year. The time horizon is 100 years. The model represents forest areas according t o seven categories (see t h e formal model description, p.6).

In addition t o t h e above, forests a r e divided into four age groups, depending on t h e species. The first is t h e period when thinning is predominant, and t h e other t h r e e are characterized by t h e final harvest.

In describing t h e harvesting policies we refer t o t h e annual growth of t h e growing stock i n t h e age group, meaning the effect of biological growth and t h a t of updating t h e age groups as time passes.

Present harvesting policies are formulated in t e r m s of t h e age groups. Harvest in t h e first age group, or thinning, is proportional t o t h e standing volume of t h e group. Final harvest is 90% of t h e annual growth of the t h r e e upper age groups in t h e case of broadleaved forests; in pine O F the hilly regions t h e figure is the same. The age distribution of low- land pine forests is very uneven, and therefore final harvest is deter- mined for each age group separately, amounting t o 509, of t h e n e t annual growth.

This harvesting policy cannot be maintained for a very long period, since t h e oldest age group would become too large. This is partly due t o the s h a r p decrease in t h e planned extension of the forest area, as well as t o t h e harvesting policy itself. Therefore, a t given intervals, t h e increase in growing stock m u s t be halted, and when an acceptable age s t r u c t u r e

is achieved one h a s t o change t o harvesting t h e a n n u a l growth by indivi- dual age groups. In t h i s c a s e , for soft, broadleaved a n d fast-growing, hard, broadleaved forests 100% of t h e annual growth is harvested from t h e fourth age group, a n d t h e increase in standing volume is supplied from t h e second a n d t h i r d age groups. For those forests with s h o r t rota- tion, t h e age s t r u c t u r e p r e s e n t in 1980 is already acceptable. In t h e slow-growing, h a r d , broadleaved forests, t h e i n c r e a s e in growing stock a n d t h e modification of age s t r u c t u r e will be halted in 1995. The harvest- ing of pine forests in t h e hilly regions remains unaltered, while in t h e lowlands t h e i n c r e a s e in growing stock will be stopped in 2040.

The above outlines two harvesting policies t h a t provide for one of t h e principles in Hungarian forest management: growing stock m u s t not decrease. The s a m e principle prevails relative t o t h e forest a r e a , and so when a p a r t i c u l a r a r e a is removed from forest cultivation during t h e final harvest, a n equal a m o u n t of land has t o be afforested in exchange.

In addition, a national afforestation program plans t h a t t h e total forest a r e a will increase. The model uses four scenarios t o assess t h e effects of different, feasible afforestation policies. The proportion of species in t h e afforested a r e a is supposed t o be constant, equal t o t h a t given in long- t e r m projections for t h e Hungarian forest sector.

The growth of forests is modeled in detail, a n d depends on t h e species, age, density of t h e forest, and t h e pollution level. This work was first done by

W.D.

Grossmann (1982), a n d more details of the mechanism a r e given in t h e forrrial description of t h e model.

To c o n s t r u c t t h e model, t h e following r e q u i r e m e n t s were esta- blished:

very detailed data for t h e year 1980 should be used (standing volume a n d a r e a for every age group and species; thinning;

total harvest of t h e final t h r e e age groups for every species).

t h e projections for t h e forest sector u p t o t h e year 2000 should be accepted a s consistent; i.e., supposing t h e originally planned d o r e s t a t i o n program is implemented and t h e original harvest- ing policies a r e in force, t h e n growing stock will reach 300 mil- lion m3 and total harvest 10 million as specified there (see Appendix).

Thus, t h e model now combines t h e four afforestation scenarios with the two harvesting policies.

3. M)RM.AJ., MODEL DESCRIPTION

The Hungarian Forest Dynamic Model is a systems dynamics model, with t h e program written in DYSMAP (Ratnatunga 1980). As is well-known (see, e.g., Forrester 1961) systems dynamics is a widely used simulation technique based on solution by successive integration of the first order difference equations:

Here t h e vector zt represents t h e state of t h e system, t h e (non-linear) function f describes t h e rules and relations in t h e system, and the vec- t o r z o is t h e vector specifying t h e state of t h e system in the initial period.

The model consists of t h r e e main blocks, which describe t h e development of growing stock, forest a r e a , a n d harvest. Forests a r e divided i n t o subsectors according t o species a n d age groups. The divi- sion according t o species is as follows:

(1) Soft, broadleaved forests (poplar a n d o t h e r soft broadleaved) (2) Fast-growing, hard, broadleaved forests (black locust)

(3) Slow-growing, hard, broadleaved forests (oak, beech, hornbeam, a n d other h a r d broadleaves)

(4) Pines in hilly regions

(5) Pines on lowlands ( t h e counties Pest, BBcs-Kiskun, Csongrdd, BCkes, Szolnok, Hajdd-Bihar, Szabolcs, a n d t h e a r e a of Budapest)

(6) Other forested areas (7) Bare land.

As t h e list shows, t h e geography of t h e c o u n t r y i s t r e a t e d a s one unit, except for pine forests. The division of pines i n t o two classes is due t o substantially differing ecological conditions and age compositions.

Other a r e a s and bare land a r e given a s constants, and a r e r e p r e s e n t e d only t o account for t h e total area. To allow t h e formulation of harvesting policies, each species i s r e p r e s e n t e d in four age groups, one where thin- ning is predominant, and the subsequent t h r e e where final harvest is predominant. In t h e notation, t h e subscript X (= S , F , H , P , B ) refers tu groups of species (see Appendix, Table k 7 ) a n d t h e subscript i (i= 1,2,3,4) t o age groups. In addition, we also use the subscripts j (= i + l ) a d k (=

i-l), a n d t h e symbol t o for 1980.

3.1

Growing Stock

Here VXliVt i s t h e volume of growing s t o c k in t h e i - t h age group of t h e X-th species. Equation (1.1) s t a t e s t h a t growing s t o c k increases by bio- logical growth ( B :) and transfer from t h e lower age group (yXnkBt), ~ ~ a n d

I I

decreases by natural decay (NX t ) , by decay due t o pollution (PX t ) , by

I * I I

transfer t o t h e n e x t age group (OXj,t), and by harvest (HX,i,t).

Biological Orowth

Biological growth is a highly non-linear quantity, described by equa- tions (1.3)-(1.7).

M x , ~

,t

=

Q x ~ x , ~ ,t (1.6)

c ~ , i , t

=

V ~ , i , t / G ~ , i , t

u~

^(1.7)

The variable FXaitt r e p r e s e n t s t h e potential volume of growing stock, s e t equal to t h e a c t u a l volume in t h e initial period (1980), and (depending on t h e delay p a r a m e t e r or adaptation t i m e ,

4 )

manipulated to give t h e highest volume possible for a given species. The growth of

FX,

is pro-

I .

portional t o t h e difference between i t and t h e maximum possible volume, which is t h e product of the area of t h e a c t u a l (1980) age and species' group (GX,,,t) a n d t h e maximum possible growing stock per unit a r e a (UX). Biological growth is then obtained From t h e potential growing stock by t h e forest growth multiplier (MXVitt).

The growth multiplier is a non-linear Function of the crowding ratio of a given class (CXBiBt), derived from functions t h a t describe t h e annual growth of the individual species (see Appendix Table A.6). The crowding ratio is defined a s t h e ratio between t h e a c t u a l and maximum possible growing stock. BX is t h e mean rotation in a given group of species. The hypothesis behind t h e formulae is that for ideal growth, a 100% crowding ratio is reached a t an age which equals t h e mean rotation time.

Fbrest Deccy

A proportion of t h e growing stock decays every year, which is represented a s a s u m of two components. The first is natural decay NX,i,t and t h e second is decay caused by pollution PXnint. Decay is pro- portional t o t h e growing stock and h e r e is assumed t o be 1% for natural and 0.25% for pollution-generated decay. Pines a r e twice as sensitive as t h e broadleaved species. Equations (1.8) a n d (1.9) describe t h i s process

wv

Standing stock in new plantations (i.e., in a r e a s where compensation or additional afforestation occurs, is taken t o be zero, a n d so does not e n t e r o u r equations. Of course, t h e r e is n o growing s t o c k t r a n s f e r r e d from t h e f o u r t h a g e group. For the r e s t of t h e age groups t h e t r a n s f e r of growing stock is described by equations (1.10) a n d (1.11).

TX,i+j,t is t h e a r e a transferred from t h e i - t h t o t h e j - t h age group.

DX,i+j,t is t h e average of t h e actual forest densities in t h e two groups weighted by t h e t i m e period of t h e groups involved (LXBi a n d LXj).

3.2 Harvesting

As h a s already been mentioned, age groups were aggregated accord- ing t o c u r r e n t harvesting policies. The first age g r o u p , therefore, is t h a t of thinning, so t h e harvest in this group is proportional t o t h e growing stock, equation (2.1).

Hx,i,t

=

VX,~ ,t EX (2.1)

Final harvest according to c u r r e n t harvesting policies is given by equa- tions (2.2)-(2.6).

Zx,s,t

=

Bx,3,t

-

^Nx,s,t

-

^{Px,3,t + Yx,z,t}

-

^{*x,4,t (2.5)}

Zx,4,t

=

Bx,4,t

-

Nx,4,t

-

Px,4,t ⁺ Yx,s,t ^(2.6) The equations (2.4)-(2.6) define t h e change in growing stock, while (2.3) gives t h e t o t a l volume t o be harvested from t h e final t h r e e age groups of a given species, equal t o 90% of t h e annual growth of broadleaved forests a n d of pines in t h e hilly regions. The role of t h e p a r a m e t e r WXni is t o control t h e age composition of t h e growing stock.

The plantation of pines in lowlands s t a r t e d some 35 y e a r s ago. As a consequence of t h i s a n d t h e different ecological conditions, t h e age com- position i s very uneven. Therefore, t h e harvest policies a r e also different, a n d allow for final harvesting of 50% of t h e i n c r e a s e of standing stock in e a c h age group.

Final h a r v e s t according t o t h i s modified policy is similarly 90% of t h e stock i n c r e a s e for soft a n d fast-growing, broadleaved forests. The distribution between age groups is, however, different, equation (2.2) being replaced by equation (2.7)-(2.10).

Jx,t = Sx,t - Zx,4,t

^(2.10)

For t h e slow-growing, broadleaved forests we have (again instead of equa- tion (2.2)). equation (2. l l)

For pines in t h e lowlands equation (2.2) is replaced by equation (2.12).

0.5

Zxvi

if t

<

²⁰⁴⁰

H~,i.t

- -1

^1.0

^ZXti

^ift

⁼

²⁰⁴⁰

Equation (2.12) implies halting t h e build-up of t h e s e pines after 2040.

3.3 Forest Area and Morestation Scenarios

The change in forest a r e a is described by equations (3.1)-(3.6).

*X,o+l,t ₌

K ~ , l , t -I- J ~ , ~ , t + J ~ , , 4 , t (3.6) In t h e s e equations

T;,~,~,~

is t h e a r e a t r a n s f e r r e d t o t h e first age group a s a consequence of final harvest (i=Z, 3, o r 4);

TX,i+j,t

is the a r e a t r a n s f e r r e d t o t h e next age group t o update t h e age of t h e forest (i=l, 2, or 3);

JXOint

is t h e a r e a taken out from forest m a n a g e m e n t for utilization in o t h e r s e c t o r s (i=2, 3, or 4);

KX,l,t

i s t h e a r e a planted under t h e afforestation program; and

TX,o+l,t

is t h e total newly planted area.

These equations ensure t h a t t h e following principles a r e observed:

(1) No a r e a is removed from t h e first age group. (2) In other age groups a r e a s may be removed, but a n equal a r e a m u s t be replanted the following year. (3) Final harvest takes t h e form of clear-cutting, a n d an equal a r e a

is replanted similarly. Updating t h e area of t h e age group is determined by equation (3.7) (i=l, 2, or 3):

TX,i + j e t

=

G x , i , t / L ~ , i ^(3.7)

The a r e a removed from forest management is 0.01% of t h e total, a s given by equation (3.8) (i=2, 3, or 4):

Jx,~

^,t

=

0.0001Gx,i ,t (3.8)

The values of t h e parameters, including t h e added areas, for t h e four scenarios, a r e given in t h e Appendix.

4.

VALIDATION

AND RESULTS

The s t a t e variables of the model a r e dependent, which means t h a t they c a n be divided into two groups, t h e vectors zt and y t . These two vectors are connected by the functional relationship yt = g (z) for all t . where t h e function g depends on t h e parameters discussed above.

Another feature of this model is t h a t a projection of t h e forest sector up t o t h e year 2000 is available, which we assume is consistent. Hence t h e r e is a function h t h a t gives the values for these projections (like total growing stock, or total harvest), which we denote by zl. Formally, h ( z i l )

=

^{z l} for t l

=

2000. Therefore t h e model has t h e abstract form given by equations (4.1)-(4.5).

Yt,

= Yo

zi*

=

^Zi

+

dtf (zt,t) (4.4)

r/t =

8 ⁽²¹ (4.5)

In t h e s e equations, t h e functions f . g , a n d h depend on t h e p a r a m e t e r s a n d equations (4.4) and (4.5) a r e applicable for all t . Now, as a conse- quence of t h e dependent n a t u r e of t h i s system, calibration required t h e parameters t o be selected in s u c h a way that:

(1) ^Equation (4.5) holds for t

=

to, so t h a t t h e complete s e t of ini- tial conditions is m e t .

(2) Equation (4.3) holds, so t h a t t h e projections a r e consistent.

The zero-th s c e n a r i o corresponds t o t h e original afforestation plan, namely t h e extension of t h e forest a r e a by 280 thousand h e c t a r e s by t h e year 2000. By c o n t r a s t , lower rates of extension a r e envisaged in t h e o t h e r scenarios, which, of course, affect t h e t o t a l growing stock a n d total harvest. Table 1 illustrates this effect which s e e m s virtu ally indepen- dent of t h e two harvesting policies.

Table 1. Effects of slower afforestation (the year 2000).

Scenario Standing stock Harvest

Comparison of t h e two harvesting policies reveals t h a t c u r r e n t poli- cies result in a dynamic growth of t h e growing stock a n d a n undesirable

shift in t h e age s t r u c t u r e , with definitely unfavorable effects in the long run (after about 30 years), such as a decline in total harvest.

The results obtained using the modified harvesting policies, which are more in keeping with the changes in afforestation rate, show t h a t these unfavorable effects can be reduced and t h e whole forest sector c a n be stabilized a t a relatively high level of annual harvest.

REFERENCES

Bencze. T. 1984. Optimal Possibilities for the Satisfaction of Timber Demand a t National Economic Level in Hungary. WP-84-64. Laxen- burg, Austria: International Institute for Applied Systems Analysis.

Bencze, T., Cs. Forgdcs, and L. Lonnstedt. 1984. The Hungarian Forest Sector System. Internal Draft. Laxenburg, Austria: International Institute for Applied Systems Analysis.

Forrester, I.W. 1961. h d u s t r i a l D y n a m i c s . Cambridge, Mass: MIT Press.

Grossmann, W.D. 1982. A Prototype Model of the Forest Sectors and Their Socio-Economic Environments. M t t e i l u n g e n d e r &ndes- f o r s c h u n g s a n s t d t f i i r f i r s t - u n d H o l e w i r t s c h a f t (Hamburg-Reinbek,

Komissionsverlag. Buchhandlung Max Wiedebusch).

Ldng, I., Zs. Harnos, A. Nagy, and I. Vdlyi. 1984. The Biopotential of Hun- gary

-

Present and Future, to appear in I n t e r n a t i o n a l A g r o p h y s i c s . Ratnatunga,

k K

1980. DYSMAP User Manual. Bradford, UK: University

of Bradford.

-

¹⁹

-

Iist of Variables Used in Main Text

Delay parameter or adaptation time

Biological growth of species X and age group i a t time t . Crowding ratio

Average of forest densities Thinning multiplier

Potential volume of growing stock Area of age and species group Final harvest

Harvest in age groups 2 and 3

Area removed from forest management ( i = Z , 3 or 4) Area planted under afforestation program

Growth period of species involved Forest growth multiplier

Loss due t o natural decay Natural decay multiplier

Loss due t o removal t o next age group Loss due t o pollution

Pollution decay multiplier

Function of crowding ratio and relative growth Mean rotation

Total harvest of last three age groups

Area transferred from i - t h t o j-th group (i= 1, 2 or 3)

Area transferred to first age group because of harvest ( i = l , 2 or 3)

Area newly planted

Maximum possible growing stock per unit a r e a Volume of growing stock

Parameter to control age composition of growing stock Group of species

Gain due t o transfer from lower group Harvest from each age group.

APPENDIX

-

20

-

Table

A1

Initial conditions ( t o

=

¹⁹⁸⁰⁾

(a) Growing stock in 1980 (million m3)

Soft, broadleaved 6.540 4.130 6.393 10.246

Hard, broadleaved, fast 15.064 6.936 9.156 2.354

Hard, broadleaved, slow 105.751 23.336 25.304 8.472

Pines, hills 16.390 4.359 1.208 0.745

Pines, lowlands 4.450 0.147 0.153 0.670

(b) Forest a r e a in 1980 (thousand hectares)

Soft, broadle aved 109.7 39.6 34.2 39.9

Hard, broadleaved, fast 159.2 47.1 50.1 12.1

Hard, broadleaved, slow 600.6 76.1 72.2 24.0

Pines, hills 141.1 11.0 2.6 1.5

Pines, lowlands 49.5 0.8 0.7 2.6

Other a r e a s (do n o t refer Bare l a n d t o age grops)

(c) Harvest in 1980 (mi I lion rn3)

Thinning Final harvest Total

Soft, broadleaved 0.409 1.034 1.523

Hard, broadleaved, fast 0.240 1.730 1.970

I-Iard, broadleaved, slow 1.298 2.215 3.513

All pines 0.282 0.252 0.534

Total 2.309 5.23 1 7.540

-

²¹

-

Table A 2 Long t e r m projections

(t =

2000)

APPENDIX

Growing stock 300 million m3

Forest area 19.800 thousand km2

Total harvest 10 million m3

Table AS. Afiorestation scenarios (Share of species in t h e afforested area (percentages): soft, broadleaved, 22; hard, broadleaved, fast, 12; hard, broadleaved, slow, 26; pines, hills, 10; pines, lowlands, 30.)

Scenarios Period Area increase

(thousand hectares)

First

Second Third

Table A4. Age groups and final harvest proportions ( L ~ , , WXIi)

Thinning Final harvest

Soft, broadleaved 0- 15 15-20 (40%) Hard, broadleaved, fast 0-25 25-30

(10%) Hard, broadleaved, slow 0-70 70-80

(40%) Pines, hills

Pines, lowlands 0-30 30-40

APPENDIX

-

22

-

Figure

A1.

Total annual growth

Soft, Broadleaved

0 5 10 15 20 25 30 35 40 Year

m3/ha

,

Hard, Broadleaved, Fast

0 10 20 30 Year

Hard, Broadleaved, Slow m3/ha

(

0 20 40 60 80 100 Year

APPENDIX Rgure

Al.

(Cont.)

Pines, Lowlands

0-,Y

0 5 10 20 30 40 45 Year

Pines, Hills

r

1 10 20 30 40 50 60 70 80 Year

APPENDIX

-

24

-

Table

115. Total production for the different groups of species.

Thinning Final harvest Total production (mS> (mS> (m3>

Soft, broadleaved 87 150

Hard, broadleaved, fast 220 380 Hard, broadleaved, slow 340 580

Pines, hills 164 320

Pines, lowlands 98 192

Table 110. Relative growth of growing stock as a function of crowding ratio (the function Q X )

Table 117. Other parameters.

Specific

Soft, broadleaved

S

25 13 0.01 0.0025 0.85

Hard, broadleaved, fast

F

30 15 0.01 0.0025 1.01 Hard, broadleaved, slow

H

85 15 0.01 0.0025 1.03

Pines, hills

P

€30 15 0.02 0.005 0.80

Pines, lowlands

B

40 7.5 0.02 0.005 0.80

Notations Used in Computer Printouts

The n u m b e r i n t h e title refers t o t h e n u m b e r of t h e afforestation scenario. JELENLEGI refers t o c u r r e n t a n d MODOSITOTT t o alternative harvesting policies.

X

=

S,F,H,P,B, denotes t h e group of species (referring t o soft, fast- a n d slow-growing h a r d broadleaves, pines hills, and pines, lowlands respectively);

I =

1.2,3,4, t h e code of age group;

LFF'OT, total forest a r e a ( h 2 )

LFXFT, t h e a r e a occupied by t h e X-th species (km2)

LFXTI, XITOT, t h e a r e a a n d growing stock of t h e age groups from t h e 1st t o t h e i-th, for t h e X-th species (km2 a n d tons), respectively,

XFVRM, total growing stock, X-th species

(ms);

FORTM, total growing stock (m3);

FRHTM, t o t a l h a r v e s t (m3);

FRI-IEM, thinning (m3);

XTOHM, total harvest, X-th species (m3);

XELOM, thinning, X-th species (m3).

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