expresii matematice ale tabelelor dendrometrice romanesti

16
369 Boletín de la Asociación de Geógrafos Españoles N.º 68 - 2015 NATUSERS’ MOTIVATIONS AND ATTITUDES IN URBAN GREEN CORRIDORS: CHALLENGES AND OPPORTUNITIES. CASE STUDY OF THE PARC FLUVIAL DEL TÚRIA (SPAIN) Mireia Alonso-Monasterio Pau Alonso-Monasterio María José Viñals Department of Cartography Engineering, Geodesy and Photogrammetry. Universitat Politècnica de València [email protected], [email protected], [email protected] ABSTRACT With the population growth in cities, urban green corridors are positioned to be one of the most in-demand green spaces, acting as recreation areas and as alternative paths for bicycle- commuters or walkers and posing new management challenges for the development of an adequate public use of these sites. However, most studies of outdoor recreation have been pursued in natural protected areas where visitors mainly develop educational/interpretative activities. In addition, little is known regarding why people use suburban green corridors and their motivations and attitudes. The initial outcomes of this research indicate that visitors of these areas primarily engage in leisure/entertainment activities and sport activities, with their primary motivations being the practice of outdoor activities and relaxation and contact with nature: they visit these places searching for an outdoor setting to pursue different activities. Therefore, these visitors could be named ‘users of nature’ (natusers) more than ‘visitors of nature’, whose traditional primary motivation was ‘to know the site’. Key words: Peri-urban green corridors, Nature users (Natusers) behaviours, Mediterranean protected areas Boletín de la Asociación de Geógrafos Españoles N.º 68 - 2015, págs. 369-383 I.S.S.N.: 0212-9426 Fecha de recepción: mayo 2013. Fecha de aceptación: febrero 2014.

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Page 1: expresii matematice ale tabelelor dendrometrice romanesti

EXPRESII MATEMATICEALE TABELELOR DENDROMETRICE ROMANESTI

Dr. doc. V. GIURGIUin calaborare cueconornist CORNELIA NEAMTU

1. INTRODUCERE

ln ultimii 25 ani, in lara noastrd au fost elaborate tabele dendrome-trice (tabele de cubaj, tabele de prorduclie qi sortare etc.) pentru princi-palele specii foresti'ere. o primd monografie a acestor tabele a fostp u b l i c a t d i n a n u l 1 9 5 7 ( P o p e s c u - z e l e t i n q i c o l a b . ) . c e r c e t d r i l eulterrioare au perrnis elaborarea unor noi tabele pentru o garnd maim a r € d e c a r a , c t e r i s t i c i g i s p e c i i ( G i u r g i u - D e c e i - A r r r r i q e s c u ,7972). Folosirea cu eficienld a ,s'istemelor de prelucrare autornartd a date-lor neceisitd ,gdsirea unor noi rmodalitdti de exprimane a relatiilor bio-metrice cuprinse in tarbelele rdendrometrice elaborate. In soiufionareaacestei probleme s-a adoptat solu$ia unui complex rde expresii matema-tice 'dte tdiferite forme, cu rc6sflgi.n{i ide negresie stabilili in baz,a informa-lii lor furnizate de tabelele,publicate in lucr:area ,,Biometria arborilor qia r , b o r e t e l o r d i n R o m d n i a ( ( G i u r g i m - D e c e i - A r m S E e s c u , l g 7 2 ) .valorile co'eficien{ilor au fost stabilite cu ajutorul ,calcuLatorului elec-tronic IBM-360 /30, prin rmetod6 statistico-matematice aclecvate *-

In cele ce urmeazd se prezintd o sintezl a cercetdrilor efectuate deautor in ultimul timp in acest domeniu.

2. BXPRESIA MATEMATICA A TABELELOR GENERALE DE CUtsAJ$I A TABELELOR DE CUBAJ PE SERII DE VOLUME

Prin cercetdrile intreprinse s-,a ajuns la urmdtoarea relalie, careexpriml legdtura statisticd dintre volumul anborelui (u) si caracteristi,cileexpli'cative d (diametrul de bazd) gi h (indllimea anborelui) :

r r : l 0 b u e x p . ( b r l o g d f b r l . o g z d f 6 r l o g h ! b a l o g z h l , ( l )sau

logc ' : b6 4-br logd* b r logzdf &3 log h{ bn logzh, Q)

' A se vedea lucrarea ,,Automatizarea 'lu,crdrilor 'de birou ro,rivind redactareaamenaJamentelor", Man;trscris, I.C.A.S., 191 4.

75

Page 2: expresii matematice ale tabelelor dendrometrice romanesti

i n c a r e :

bo, br, bz, bn qi ba sint coeficienlii de regresie din tabelul 1, sta'bililipentr'u ZO specii forestiere mai importante. ln baza acestei ecuatii a fostintocmit un program, dupd care po,t fi elaborate tabele de c.tibaj cu douiintrdri (Programul TAB.C).

conlinutul tabei,elor de cubaj, pe serii de volume, corespunde urmS-toarelor expresii cunos'cute (G i u r g i u, 1965) :

Arborete echiene

- categorii de diametre mai mici decit.diarnetrul rnediu

, : !_ ,0 .162 r , i 62 {+ i ' i 0 ,186 , . *o [ - r ,as { { ) ' l } r< (3 )" - l \ u t

' t \ D / . 1 , '- categorii de d'ametre mai mari decit diarnetrul mediu

Iu :

i ( r , 45 r - 0 ,0167D r -0 ,000133 t , [ ( * ) ' - r

] + r ] r ' ( 4 ]

unde

d reprezintd categoria de dia,rnehe [n cm;D diarnetrul mediu ln cm;D - vol,urnul ln m3;K 'un pana,metru stabilit, in funclie de specie, dirarnetrul rnediu qi

de ind,llirnea rnedie, folosind tabe,le speciale (Giurgi,u, 1965, 19/i2).

Ecuafiile (1) Ei (2), prezent'ate mai sus, oferi o noue solulie pentrudeterminarea coeficientului K, fdrd a mai fi nevoie de folosirea tabelelorAstfel, coeficientul K rezultd din

l o g K : u i * b r l o g D * b r l o g z D * b r l o g H * b s l o g z H , ( 5 )

in care

D neprezintd diarnetrul 'rnediu efectiv, determinat pe teren ;H lndllimea medie 'corespunzd'toar'e acesturi diametru mediu;

b'0, br, b2, b3, ba - coeficientii din tabelul 1.

In ceea ce privegte arboretele pluriene, s-a propus urmdtoarPaecualie :

rs : (ao* ag * a"d' + .-. { ard?) K, (6)

unrde coef ic ienl i iau, at . . .az sint cunoscu{i (Giurgiu, 1965, 1972) '

Pentru coeficientul K vom folosi acum urmdtoarea relati€, bazatitpe ecualia (2) :

l og ( : b ;+ b r l og50*b r l og250*b3 log Hso* b t l og2 l l so , g )

in care valoarea de 50 r'eprezintd categoria de diametre indicatoare' iar

iI;o - indllimea medie corespunzdtoare. Aceasta din urmd se calculeazi

76

Page 3: expresii matematice ale tabelelor dendrometrice romanesti

I

Coeficien{ii bt din ecuafiile I qi 2Tabelul l

Coei ic ien{ i i

L2Tl3 lt4i

i;l17l18tr q l' " 1

2012rl,91

231,41- - lq R i

2612712812sl

I

MolidBradLaricePin silvestruPin negruDuglasFrgMesteaclnAnin albSalcie cipreascdPlop tremuritorGorunCarpenFrasinStejarPalt inTeiJ ugastruCerAnin negruUlmSalcimStejar pufosStejar brumdriuPlop alb qi negruPlop euramericanSalcie sdmin{dSalcie sul inariGirni{d

0,000094640,000045200,000028220,000148080,000108920,000044770,000075700,00008r410,000650130,000r 15850,000076040,000070310,000073640,000306480,000088390,000353750,000041240,000205300,000199200,000086660,000039920,000469030,000351640,000071880,000180590,000414860,000042810,00007325

S P E C I Ab,

- 4,0239-4,3449*4,5494-- 3,9295- 3,9669- 4,3490* 4,1209- 4,0893-3,r870- 3,9395- 4,1 190- 4,t529- 4,1329- 3,5136- 4,0536- 3,4513--4,3847- 3,8876-3,7007- 4,0622- 4,3988- 3,3288-- 3,4539- 4,1434-3,7433- 3,3821- 4,3684-4,1352- 4,0208

r,93412,13542,20601,8341I ,9701I,8688r,37912,2480I,67501,66881,78t22,?n,822,t3021,26761,8905l,0200I,93021,85592,01401,71482,1569I,8070I , l l l 9I,44861,9342I,44662,0766l,5598I ,7079

-0,0722.- 0,1067-0, i l36- 0,0448

0,01020,04240,2127

- 0,20620,10010,10900,0528

- 0,1008-0,0013

0,31020,04690,39970,02090,03940,06020 , l 0 l 4

-- 0,09330,02920,31080,02040,00130, r089

: 0 , 1 2 9 60,03020,0081

0,63650,93801 , 0 1 1 50,3r l50,48581 , 1 4 1 lI , r 9920,1946

- 0,49900,77810,85330,50590,45r40,49290,80590,6660I,29000,5945

- 0 ,1 1080,80101,0728

- 0,41550,53561,4084

- 0 ,0161- 0, 1963

0,68430,85720,9158

0,17200,02280,01290,35250,1330

- 0,1047- 0,0584

0,4t470,59020,02690,06540,12050,17320,0962

- 0,00450,0210

- 0, 19030,07420,48r I0,0530

- 0,07080,54550,21390,04090,40990,56810,27450 ,17910,0096

in furrclie de diametrul central (D) qi de indllimea corespunzdtoare (II),efectiv mdsurate pe teren. In acest scop s-a propus ur.rrr5lotrrea relalie :

, , H (cr l c1D - f c"Dz1nuo : ___

Dr_

unde valorile coeficien{ilor cs, c1 gi c2, stabilite prinmatem,ati'ce, sint prezentate in tabe,lul 2.

(8)

prelucrdri stat ist ico-

3. EXPRESII MATEMATICE PRIVIND CURBELE DE DEZVOLTAREALE PRINCIPALEITOR CARACTERISTICI DENDROMETRICE ALEARBORETELOR

Cercetdrile intreprinse au mai permis stabilirea de expresii mate-matice pentru curbele rde cregtere gi dezvoltare, privind principalelecaracteri'stici biometrice ale arboretelor echiene. De asemenea, au fost€xprimate matemati'c cele mai importante relafii dintre aoeste ,caracteri'strcl{tabelul 3).

t t

Page 4: expresii matematice ale tabelelor dendrometrice romanesti

Tabelul 2

Coelicienfii ct din formula (8)

.- H (cs* cr D I cz D2)nuo: -------F--

Tabelul 3

Expresii matematice privind curbele de dezvoltare ale principalelorcaracteristici dendrometrice ale arboretelor echiene

D e n u m i r e a r e l a { i e i Expres ia matemat icd

Numdru ltabe lu lu i

cuprinzindrialori le

coeficienl i lorde regfesie

383, I 107

0 ,761180,8310

Variat ia ini l t imii mediide virsta arboretului

T2(f1) inQ) a l b T * c T z

H s : a o * a r H

a 6 * a r I r I a z l T

l -

volumul la hectar (V),bazd (G) qi tndlfimea

a - l b T * c T '

G n - d o l a t H + a r H z

V n - a o * a f i + a z H z

V : G ( a o * a 1 H * a n H z )Rela{ia dintre

suprafafa demedie (11)

dintre indl{imea superioardqi inil{imea medie (1/)

Relafia dintre clasa de produc{ie abso-lutd (Io) 9i clasa de producfie rela-t i vd ( / " )

Variat ia diametrului mediu (D) infunc{ie de virsta arboretului (?)

Relatia dintre suprafal,a de bazk lahectar (G") Ei indlfimea medie (H)

Relatia dintre volumul la hectar (V,,)qi inil{ imea medie (l/)

78

Varia{ia cregteri i curente (1,) in funcl iede virsta arboretului (?) log i , : a* bT - l - c log ?

Page 5: expresii matematice ale tabelelor dendrometrice romanesti

Prin intermediul relaliilqr de bazd din tabelul B, pot fi calculate Eirestul valorilor caracteristicitror biornetrice cuprinse in tabelele de pro-duclie romdnegti. De exemplu, prin integranea funcliei creqterii in volurnpoate fi 'determinatr produclia total5 ; o precizie suficientd se obline qiprin insum,area creqterilor pe perioade rde 5 sau 10 ani. crestere,a mediea producliei to,tale se obline prin raportare,a la virstd a pr,oducliei totaleastlel calculat5. Maxiimul cregterii medii indicd virsta exploataibititdtiiabsolute.

Valori aproxirnative ale producliei interrnodiare cumulate se oblinfdcind difer,enla 'dintre pno'ducli,a totalS gi produclia principald la virsta T.

Clasa de Pnorduicfl. se determind prin inter,polrare, folosind primarelalie din tabelul i't

Pentru cunoaEterea volumului la hectar a prorducliei principale ladiferrte virste, pe clase ide pro'duclie, se va detenrnina ini{ial fndllimearn.-edie, dupd prima r"elalie din tatbelul 3. In continuare, prin simplaimpdrfine Ia virstS, se poate detenmina cregterea medie a produ,cfiei prin-cipale. Dacd prirn ? vom inlelege virsta exploatabilitdlii, vom oblinecreqterea medie la exploatabilitate a proidu,cliei principale. Creqtereacurentd a producliei principale va rezulta din diferenla volumelor rea-Iizabile pe o anumitd perioadS.

Tot atit de simplu pot fi stabilite valorile pentru : nu,mdrul de ar-bori Ia hectar, indllimea redursd, coeficientul de form5.

Expresiiie matematice prezentate mai sus neprezintd fundamentulbiometric al introrducerii sisternelor de prelu'crare automratd a datelor laarnenajarea Ei punerea in valoare a p5durilor. Au fost deja folosite laelaborarea urmdtoarelor programe (s'crise in limbajul FORTRAN saucoBol,) :

- programele privind 'calculul volumului total gi pe sortimente,destinate amenajdrii qi punerii in valoare a pS,durilor (programele APVsi AMEN) * ;

- progra,mul descrienii parcelare (PRELFORT) *;

- prograrnul privinrd inio,cmirea evidentelor statistice in amena-jament (PROIECT) *;

- progra,mele privind cal'culul posibilitd{ii la p6durile de codruregulat (POS-VE qi PROIECT-9).

Sfera de apli'cabilita'te a expresiilon matemati'ce prezentate este cumult mai largd ; pot fi folosite qi lra el,aborarea de mo'dele de programarematematicd sau de simulare, precum si ,in alte 'domenii a1e cencetdriloropera!iona1e.

* A se ve.dea lrrcrarea [.C.,A.S. ,,A)Lr,totrnatizarea lucrdl'ilor 'de ;bi,r"ou privi,ndintocrnirea arnenajarmerntdlor" (G i u r g i u qi colab., '1974, manuscris), prezentatdln rezum,at Ei in prezentul volm,rn (Seceleanu q.a., 1975).

79

Page 6: expresii matematice ale tabelelor dendrometrice romanesti

Tabelul 4

Coelicienfti a, b pi c din ecualia

H :a * b x * c x z

(prin x se in{elege virsta arboretului T)

C l a s a d e p r o d u c { i e

S p e c i a

dlb lc l

abL

ab

bc

ab

ab

aD

u

a.bo

ab

17,02880,42790,0209

37,60580,31560,0230

2l,67900,07160,0239

12,30840,53300,0251

12,48450,62310,0273

20,1660o,52790,0221

4,68650,69280.0242

5,7814I,00590,0222

5,74860,90650,0270

4,55990,82190,0257

20,73160,55r60,0235

47,85830,33220,0257

24,95230,1 6430,0266

14,32630,73940,0281

t7,0t760,72450,0317

25,62200,60480,0248

Fag

Mesteacin 5,39660,83660,0262

8,73001, t 5940,0249

5,2256|,13770,0297

5,95700,92780,0278

r r l r r r l ru

27,6n2 | 4t.2270 | 76,e0230,7157 | 0,94810 , 0 2 6 9 1 0 , 0 3 1 5 1 0 , 0 3 8 9

65,4206 I 99,50820,3124 | 0,09490,0293 | 0,0348

3l,3l0l | 42,79t0 | 65,67050 , 2 3 8 7 1 0 , 3 2 5 7 1 0 , 4 8 1 20 , 0 3 0 7 1 0 , 0 3 6 5 1 0 , 0 4 4 3

17,91l l | 25,4t7t I 49,92931 , 0 6 8 2 1 1 , 6 0 2 5 1 2 , 4 8 5 t0 , 0 3 r 8 1 0 , 0 3 6 7 1 0 , 0 4 5 5

Pin silvestru

22,49530,92450,0371

34,8763o,70970,0281

5,73951 ,07190,0281

13,5557r,39690,0280

9,51991,22420,0353

I ,1092I,94230,0312

41,73952,24530,0376

n,3220 | 18,89401,5789 I 1,88050,0409 | 0,0511

8,2230 i 9,70131,3992 I 1,79530,0322 | 0,0349

Gorun (simln{d)

Corun (ldstar)

BO

Page 7: expresii matematice ale tabelelor dendrometrice romanesti

Tei argint iu

Girni{d

Salcim (plantat ie)

Salcim (l istar)

15,2t750,96650,0326

26,64761,09910,0362

4,24710,89070,0 96

- 0,38150 ,61910,0326

2t,76560,90850,0431

- 2,0141I ,61 290,0384

Stejar (simln{i)

Stejar (ldstar)

16 ,7 l6 l0,46680.0238

21,09490,89340,0287

3,61680,49760,0166

_- 0,10500,36220,0255

2,46190,11720,Q272

0,86050,26280,0246

2l ,86600,53870,0259

' 7

" 9 10,80050,0301

8,06990,77770,0280

9,79010,89920,0290

30,99600,54610,0289

10,40700,93780,0334

14,31640,80660.0321

4,230 l0,14730,0374

0,96830,31850,0266

44,78800,54480,0327

20,4r690,94370,0386

22,45860,89980,0367

23, I 4351,05420,0370

25,3063|,46250,0397

9,31090,93120,0282

- 0,75380,91330,0370

5,49400,2t940,0453

I ,61550,33530.0325

I,38660,38280,030E

2,23840,53200,0379

2,48750,21240 ,061 I

20,3987l , 31620,0659

2t , t8762,7158o,o746

8t,47000,22370,0389

38,52330 , 9 1 1 10,0455

14,79391 ,71270,0378

99,1709- I,0889

0.0595

5,98550,6456

_ i.0281

5 ,01190,70820,0251

5,51720,87990,0257

22,7737|,02t20.0317

I ,15850,3r340,0280

I , 13820, I 2830,0444

25,884 II q l 4 G

0.0445

Plop alb gi negru

abC

o

bc

b

ab

ab

ab

abc

3,72990,67240.0176

- 0,39460,49820,0273

0 ,61 l40,2965o,0224

3,08250,13570,0314

0,68780,28250.0229

3,76090,1923o,0472

7,95930,36900,0569

2,14380;46970,0372

4,59100,70360,0469

4,13330;35330,0728

Plop e .a . (3 -5 m2)

P lop e .a . (6 -9 m2)

Stejar brumdriu

Stejar pufos

0,53020,24810,0203

0,46550,26000,0198

0,88160,33420,0260

0,98510,08170,0398

9,77920,48290,0375

10,08241,23260.0440

9,03720,79680,0416

1 ,47130,40520,0320

I,59400,16400,0513

12,3465I,02560,0507

13,29392,t5790,0580

4l,9899I,95330,0915

23,98985,44830,0768

10,9572I ,6156o.04s7

Salcie (sdminfd)

Salcie (listar)

8 t

Page 8: expresii matematice ale tabelelor dendrometrice romanesti

Tabelul 5Coelicienfii ao la at din ecuafia:

H " : a o I a r H

C o e f i c i e n t i iS p e c i a

MolidBradPin si lvestruPin negruFagMesteacinGorun simin{dGorun listarCarpenStejar sdmin{iStejar listarTei argint iuCerGlrnildPlop alb qi negruPlop euramericanPlop euramericanSalcie sdmin{dSalcie lSstar

(3- 5 rn:)(6-9 mz;

2,3003 ,190| ,6741,3292,723I , 1821,200t ,4141,626r,784I ,9971 , 1 6 5r , 4 1 91 'LA

0 ,5140,6690,607| ,4480,538

I,0300,991I,025I,0340,9731,0421,000I,0040,9890,9830,979I ,010I,004l ,0021,050I,048I ,051I,009I,038

Tabelul 6Coelicienfii at), at li an din ecuafia:

I a : a o * a r l r l a r l l

C o e f i cS p e c i a

MolidBradPin si lvestruPin negruFagMesteacdnGorun sdmintdGorun ldstarCarpenStejar simin{5Stejar l istarTei argint iuCerGlrnildSalcim plantal i iSalcim l-dstar

'

Plop alb gi negruPlop euramerican (3-5 m2)PloP euramerican (6 9 m2)Salcie sdmin{dSalcie ldstarStejar pufosStejar brumdriuLarice

20,345616,710816,419914,297013,95r 5I I,583612,276412,358812,210915,361013,846016,773912,48069,3t27

24,203823,9t5826,472137, I 10031,727534,942833,693312,4E06I 2,480620,3456

- 3,3545b- 2,62872- 3,48463-3,05315

2,18036- 1,80568- 2,06178-2,14526- 1,80222* 2,83788-2,734ffi- 2,95364- 2,01686- 1,29884- 5,20589- 6,04430- 5,88632-7,24100-6,46297- 5,89389- 6 , l 9 t9 l- 2,01686- 2,01686- 3.35458

0,090910,095090,165010,160370,051270,032160,072720,077840,075520,144490,157560,145900,058260,034950,220970,386460,309530,308640,310480,224720,231670,058260,058260,09091

82

Page 9: expresii matematice ale tabelelor dendrometrice romanesti

Coeficienfii I, D fi c din ecuafia:

D :)cz

a * b x * r r ' '

pe specii ;i clase de produc{ie(prin x se inlelege virsta arboretului T)

39, I0,680 ,0121 0,01

t0,7779I,00270,0124

I 6.7286

0,01

19.24210 ,0

36, 53,6 r l1 ,09510,01 0 ,01

45,0,

9L 74 44,56

Tabelul 7

8,G591I ,7381

I ,0,0 t

- 6o .0 , 0 1 1

t 7 , l0,7t0,0

Mesteacdn I4,8531 , 1 4 30,021

I0,80,0

abc

.tbc

abc

ab

I ,0.01

6,65"141,32710,0259

I,88390,0132

- il,50243, l38l

S p e c i acoer ic i - |

en l i i I

z l

0,610,0184

Pin silvestru

Pin negru 23,33540,9441

3,96I

0,01

I ,5310,0

Gorun (sdmin{d)

Gorun (listar)

39,854

130,085r

79,8881

30, l8l ,800.02

0,01

B3

Page 10: expresii matematice ale tabelelor dendrometrice romanesti

Stejar (sdminfd)

?abL

14,659t1,022i0 ,01 I I

18,8107I ,1 4860 ,0116

5

23,45141 ,31020,0122

6

33,29131,425C0 ,0131

7

50,516l ,4430 ,014

Stejar (ldstar) ab

- 2,20871,46770,0149

- t , 54I ,590,01

0,86I ,640.01

4 , 1 6 1 5I ,71850,0190

5,35871,8951

Tei argint iu ab I , 31

0,01

2,9943I ,50010,016c

3,58621,72770,0160

10,5392I,58600,0195

I I,5603L 4 t 9

0,0 i 63

Cer ab

0,86'- 1,66(

0 ,011

2,7664t,75260,0128

4 , 11 , 90,0

16,32871,76230,0176

23,7$A1,84390.0208

Girni{d ab

16,3356I ,8 r460.0161

t4,47002,05800,0154

r 5,399 r l

0,01

t6,77922,37350,0167

13,74022,72940,0169

Salcim (plantatie) ab

- 0,7320,8440,007

1 ,01530,78380,0166

1,17840 ,0151

0,1097I,36930,0222

3,34521,42930,0368

Salclm (listar) abU

0,8900,012r

- 1,28630,90630,0174

- 2,32| , t 70,0r

- 1,0372I,28340,0340

- 2,5982t ,87140,0330

Plop alb ii negru ab

2,88940,348',t0,018t

3, l9 l t0,373t0,021:

3,81000,41860,0229

4,36060,4571.0,0265

6,49030,531,0,0297

Plop e.a. (3-5 mz)b

- 0 ,1320,4850,007

- 0,20570,u740,0089

- 0,14420,60710 ,01 l6

0,31840,64170,0169

0,50140,E0260,0198

Plop e.a. (6-9 m'z) abL

- 0,06480,45830,0106

- 0,21950,55930 ,01 l9

0,10290,60800,0164

0,73630,66480,0226

Salcie (simlnfd) ab

0,2750,5150,010

0,59230,58360 , 0 1 1 I

1,25200,65540 ,01 r5

2,46600,73110,0120

5,312C0,764C0,013,

Salcie (listar) a,b

- 0,24970,35510.022?

- 0,36170,45940,0229

- 0,54460,62530,0222

- 0 ,41 l :0,853t0,020(

0,7751I, l80i0,016[

Stejar brumdriu ab

700

7,49810,75830,0279

7,7768l,06260,032c

8,67241,50630,0392

t8,t44tt,77740,059'i

Stejar pufos ab

9,9919I ,26310.0174

E,4955I,58250 ,021 I

8,97251,825e0,0274

25,4155l,25860,0459

4l,464C0,796t0,066(

Page 11: expresii matematice ale tabelelor dendrometrice romanesti

Coelicienfii ao, ar |i a, dln ecuafla

G, : ao+ a f i * a rHz

7,9t9714,9461

- 5 ,1 l 9 l6,28896,28892,79t5

- 0,4646l ,51333,2767

- 2,5303t0,27849 ,81 l04,66192,61906,4594

- 0,9352- t,3047- 0,8214-8,4347-8,1533

0,6666- 1 1 , 8 4 1 5

0, I 5944,2237

2,22809l,389303,094541,549741,54974I ,71004r,50605I,36406t,25952I ,976100,544600,547241,b227I ,31 1290,942431,16597l,07358I ,382142,683092,351732,000004,095032,73201,9241

Tabelul 8

Tabelul 9

- 0,020310,00l38

-0,034920,002510,00251

- 0,01582- 0,0021 I- 0,00143- 0,00073- 0,03304

0,018620,01783

- 0,01070-0,00060- 0,00743

0,002260,002720,00041

- 0,02801-0,02527- 0,00178- 0,06441- 0,0563- 0 ,0121

C o e f i c i e n t i iS p e c i e

MolidBradLaricePin si lvestruPin negruFagMesteacdnGorun sdminfdGorun idstarCarpenStejar sdmintdStejar l istarTei argintiuCerGirni{dSalcim plantat i iSalcim l istarPlop alb gi negruPlop euramerican (3-5 m2)Plop euramerican (6-9Salcie sdmin{dSalcie l5starSteiar brumdriuStejar pufos

Coelicienfii ao, at li a, din ecuafia

V: au+ arH + arHz

C o e i i c i e n t i iS p e c i a

MolidBradPin si lvestruPin negruLariceFagMesteacdr,tGorun sdminfdGorun ldstarCarpenStejar sdminfiSteiar ldstarIe l a rgrn i lu

- 86,2859-71 ,7109

- t8,7507- ]IB,7LC7- 9 l ,0015'-22,9t04- 36,6934- 14,5740- r9,3945- 38,0362

26,638714,6984

-_ 60,839t

23,387212 t ,41518,6577 |8,65771

t7,351208,995127,927735,482676,83618

ll,023441,290042,26050

16 ,13916

0, I 50240,23580,523960,523960,329200,382130,314350,538390,477750,172590,651820,595370 , 1 3 9 1 9

B5

Page 12: expresii matematice ale tabelelor dendrometrice romanesti

(Tabelul 9 cantinuare)

C o e f i c i e n t i iS p e c i a

CerGirnifdSalcim plantaliiSalclm listarPlop alb 9i negruPlop euramerican (3-5Plop euramerican (6*9Salcie siminfdSalcie listarStejar brumdriuStejar pufos

mt)m2)

28,98109,0365

- 9,62252,1022

- 5,6800- 16,1468- 2,6032-42,2781- 58,9305- 8,1739

I ,9881

-0,259522,798102,99316t,261233,007573,350590,74410

10,9295914,344488,56366,5714

0,605880,609890,418830,41907o,464520,510390,497900,309330, 16r450,37690,7262

Tabelul I0

Coeficientii ttot d.t li a, din ecuafia

V -- G(ao + aLH * azHz)

S p e c i a

jtlolidBradLaricePin silvestruPin negruFagMesteacdnGorun simin{iGorun ldstarCarpenStejar simtn{dStejar ldstarTei argintiuCerGirnifiSalclm planta{iiSalcim listarPlop alb gi negruPlop euramerican (3-5 m2)Plop euramerican (6-9 m2)Salcie simin{iSalcie ldstarStejar brumiriu

0,5450,6330,4390,530

0,5570,4430,5620,5560,5720,6000,6290,4090,2780,7230,3910,2540,3590,2030,0730,3200,2750,22t5

- 0,00360,006

-0,00062-0,00388

-0,0017- 0,0026- 0,0026- 0,0017-0,0022-0,0038- 0,0039

0,00070,0032

- 0,0073- 0,0007

0,0028- 0,00046

0,00400,00780,0015

- 0,00160,0078

C o e f i c i e n t i i

0,4330,0450,4900,485

-0 , l g l0,8140,8450,5620,3360,386

-0 ,165I,9542,497

- 0,520I,7933,049l ,898| ,8752,6661,759l ,7652,1874

86

Page 13: expresii matematice ale tabelelor dendrometrice romanesti

Tabelul I1

Coeticienfii o, b gi c din ecuafia

log ip : a* bT * c log I

Spec ia

I

Coe{i-c ient i i

,

Clasa de producfie

I l r l l r u l ' u l val4 l ' l '1 ,

Molidab

0,30990- 0,01219

0,93303

0- 0,0130

1,0988

-0,48808- 0,0 1440

1,38492

-0,95469- 0,01497

r,61945

* 2,09076- 0 ,01813

2,25955

Bradab

-0,40782- 0,01323

I ,37155

-0,67940- 0,01327

I ,48861

- I , 15145- 0,01434

1,75255

- I,90200- 0,0r 610

2,19346

-2,67789- 0,01708

2,59800

Pin silvestru bc

*0,26844- 0,01841

I,37828

* 0,58559-0 ,0191 I

|,52937

- 1,74218-0,02549

2,34615

- 1,09817- 0,01897

I ,68170

-2,49539*0,02746

2,63953

Pin negruab

-0,52858- 0,01913

I,52054

- 0,50073- 0,01790

I,40993

-0,63239- 0,01670

I,39038

- 0,97308- 0,01719

1,52875

-2,85738-0,02773

2,86712

Fagabc

* 0,62146-0,01271

I,43504

* 0,69756-0,0t244

t,42281

- I,05951- 0,01341

I,6r570

- 2,20835-0,01753

2,35269

- 2,96893- 0,01974

2,79457

MesteacinabL

- 0,10573--0,02482

r,30523

- 0,58714*0,02833

I ,661 56

- 1 , 1 0 1 0 6-0"03138

2Sr848

- I ,23100-0,0271&

I,94668

- I ,21085- 0,02069

l ,68221

Gorun (simln{d)ab

0,37136- 0,00756

0,62963

o,14797- 0,00821

0,73078

- 0,41450- 0,01042

|,07976

-0,58770- 0,01027

1,1 1280

- l ,13596-0,01068

1.34977

Gorun (listar)abc

0,31084- 0,01 155

0,75270

0,10345- 0 ,0121 I

0,84642

- 0,25868-0,01357

I ,05191

-0,60574-0,01499

I ,23831

- I , 31614- 0,01937

|,71375

Carpena 0,39524

-- 0,01 I 530,70737

0,18879-0,01207

0,81420

0,01633- 0,01206

0,88175

-o,32072- 0,01294

1,06965

- 0,68163-0,01384

1,26947

Stejar (sdminli)abc

- 0,86014- 0,01630

r,69759

- 1,33934- 0,01733

I,95925

- 1,73722- 0,01854

2,18054

- 2,28098- 0,02000

2,48425

-2,64546- 0,02062

2,64793

Page 14: expresii matematice ale tabelelor dendrometrice romanesti

Stejar ( ldstar)

Tei argint iu

Plop e.a. (6'- 9 ma)

Salcie (sdminfri)

Salcie ( ldstar)

abc

a.b

- 0,25932- 0,0 l7 l8

r,28080

-0,15767- 0,0 r 502

I , l 0 l 9 2

- I,36400- 0,0 l68l

1,84472

0,00926-0,43757

I,53201

0,76802- 0,02205

0,702t6

- 0,46592- 0,01002

1,25624

- 1,04636- 0,01842

1,62290

- l,80873-0,02313

2,15407

- 0,17249- 0 ,01710

I ,29513

r,06637- 0,01877

I,796t3

0,62392,-0,01457

l , 3 r646

- 0,787 l5-0,01476

|,35727

- I ,19264- 0,01666

t.59t27

o,3e6r7 | o,rorrn-0,03270 | - 0,03294

1,0820e l ,

1 ,064B0

- I I Rtt.)- 0 ,01505

I,63682

0,01869- 0,02453

I,20493

0 ,491190,025130,87012

- I ,26016- 0,01452|,6t292

- 0, 18654- 0,02235

| , t7491

0,22067- 0,02708

0,97926

- I ,169780,01287l ,441 86

- 0,40396- 0,01978

1,09209

0,06830- 0,01239

0,57566

- 0,63450- 0,03935

I ,69713

I ,31488- 0,0 1920

0,33136

t,004970,029790,63904

0,59960-o,04224

I,04553

- 0,28t09- 0,06699

r,99885

c

bC

abC

I,0841 3- 0,0261 I

0,5671.1

0,81098- 0,03382

0,80171

0,333 r 9- 0,04959

1,30797

- 0,160610,05918I ,71606

|,53492-- 0,028r 3

0,22764

1,14375'- 0,04062

0.$7267

0,50796--0,06454

I.46786

Girn i ld

Salcim (planta{ie)

Salcim (ldstar)

Plop alb si r .egrrr

Plop e.a. (3-5 mz;

Tabelul 1 I (continuare)

- 0,32021- 0,04635

t,95270

- 0,30876- 0,09239

2,44636

- 1,45136- 0 , 1 2 1 1 3

3,69553

- 1,06989- 0,01642

I,67230

0,30623- 0,01801

0,6551 1

0 ,561 l7-0,01775

I,50984

--0,42282-'0,0 t 434

|,24047

- 0,22776- 0,01357

I , l 4 3 l l

- 1,42755- 0,01788

l,95560

0,17419- 0,04199

l .54915

0,44664- 0,04151

1,27863

I ,01 233-0,02047

0,57665

| ,37012- 0,02013

0,38606

1,24531-0,02290

0,46953

0,89755- 0,03260

0,95515

BB

Page 15: expresii matematice ale tabelelor dendrometrice romanesti

BIBLIOGRAFJE

1. ArrnSgescu, S. Taibele de pnodrucfie, In, lu,crarea: ,,Biometria arborrilor giarboretelor din Romdnia", E lit. ,,Cenes", Bucrureqti, 1972.

2. Deoei, I. Taibele generaile de cu'baf. In lucrarea: ,,Biorne,tria arborilor gi arbo-retelor dln RornAnia", Edi't. ,,Ceres", Bucu,reqti, 1972.

3. G i u r g i u, V. Algoritrni pentnr calcule derndrornetrice, I.N.C.E.F., Bucureqti'1965.

4. G i,u r g i u, V. Relatii biornetrice pentnr redaotarea automatd a amerrrajarnen-tului. Revista pddurilo,r, nr. 3 qi 4, 1W3.

5. Giurgiu, V. O expresie m,aternatic'd unicd a rela$iei volum-diarnetru-Xn6,llirnepentm maj,oritatea speciilor f,o,restiere din Romdnia, Revista pddurilo,r nr. 4.1974.

6. Giurgiu, V. gi colab. A'utomatizarea lucrdrilor privind redaetarea amenaja-rnentelor. Ma,nuscris, I.C.A.S.. Bucure$ti, 197t4.

7 . G i ru rg iu -Dece i -Ar rndqescu. B iomet r ia a rbor i lo r $ l a rbore te lo r d inRomd,nia, Edit. ,,Ceres", Bucu,reqti, [972.

8. Popescu-Zelet in, [ . q.a. Tabele dendrometrice. Edit. agno-si lvicd, Bucureqti ,1557.

MATHEMATICAL EXPRESSIONS OF THE ROMANIANDENDROMETRICAL TABLES

- Summara -

On the jbasis of the rirnf,ormation given by the presedt dendrometrical tables,realiserd in our country lduring the rtrast 25 years, it has tbeern elabora'ted a unitarysystem of mathema'tical expressions of the most usual bio,metric.al relations necessaryin the automa'tic corrrpi:ling of the management. This u'ni,tarry sJistern odfers, itn aetNlcirse arrrd c,ornrcentrarted forrn, ait lerast the sarrne nuimber oif irnfo,rmration as areincluded i,n the cornplex of, dendnometrical tables elaborated in the last decadesfor the 29 forest spe'cies ttf economic irrlportance in our country.

The systein cornprises :- the rnathema.tical expression of the content of the general volume tables

(for.mrulas t a,nd 2), together witLr the regression coefficients of, thi'sexpression (table 3). At the same time a program was ela'borated forcornputing the general vo.Iume tables wi'th two inpruts (program TAB. C) ;

- the regression equatio,ns of the volmme curves for even aged starnlds (for-'

mulas 3 ,anrd 4) and uneven aged stands (formar,la 6), previously elaJborated,co,mpleted wittr new solmtions as regards the relatio'n betwee,n K coefficientanrd the sespective factorial characteristics (forrrnulas 5, 7 and 8) ;

- the rnathernatical expressions of the develorpment land growth curves con-cerning the even stands 'of the rnain forest species for which yield tableswere elaborate (the t,ormnrtras in Tahle 3). These relations express quiteaccuaretly the cunres of height, d'iametre, basal are,a, and volurne incre-,ment, the curves Df volume ou,rrent incrernent ; they also provide sufficientinforrnation on the total and interm.ediary yield, the mean increases of thetotal and interrnediairy yield, the absolute felling a.ges, et'c.

The pr,oposed mathe'rnatical expressions were rusdd in the etrabomation oiseveral compu,ier prdgrarns for forest rnanagernent amd twming to good acrcou'nt(prograirns AF|V, AMEII, PROLECiI, ,PREIJF,ORi|, POSIB-V.E, et'c); at the sarne timethese expressions are of par,ticular irnportiance to the application in Sllvicultureof operational reseanches. especially in elaiborating certain si;rnulation models.

B9