expresii matematice ale tabelelor dendrometrice romanesti
TRANSCRIPT
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
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
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
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 ?
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
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
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
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
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
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(
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
(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
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
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.$7267
0,50796--0,06454
I.46786
Girn i ld
Salcim (planta{ie)
Salcim (ldstar)
Plop alb si r .egrrr
Plop e.a. (3-5 mz;
Tabelul 1 I (continuare)
- 0,32021- 0,04635
t,95270
- 0,30876- 0,09239
2,44636
- 1,45136- 0 , 1 2 1 1 3
3,69553
- 1,06989- 0,01642
I,67230
0,30623- 0,01801
0,6551 1
0 ,561 l7-0,01775
I,50984
--0,42282-'0,0 t 434
|,24047
- 0,22776- 0,01357
I , l 4 3 l l
- 1,42755- 0,01788
l,95560
0,17419- 0,04199
l .54915
0,44664- 0,04151
1,27863
I ,01 233-0,02047
0,57665
| ,37012- 0,02013
0,38606
1,24531-0,02290
0,46953
0,89755- 0,03260
0,95515
BB
BIBLIOGRAFJE
1. ArrnSgescu, S. Taibele de pnodrucfie, In, lu,crarea: ,,Biometria arborrilor giarboretelor din Romdnia", E lit. ,,Cenes", Bucrureqti, 1972.
2. Deoei, I. Taibele generaile de cu'baf. In lucrarea: ,,Biorne,tria arborilor gi arbo-retelor dln RornAnia", Edi't. ,,Ceres", Bucu,reqti, 1972.
3. G i u r g i u, V. Algoritrni pentnr calcule derndrornetrice, I.N.C.E.F., Bucureqti'1965.
4. G i,u r g i u, V. Relatii biornetrice pentnr redaotarea automatd a amerrrajarnen-tului. Revista pddurilo,r, nr. 3 qi 4, 1W3.
5. Giurgiu, V. O expresie m,aternatic'd unicd a rela$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