Characterizing thinning treatm ent

In section 4 .3, it is described how the th inning treatm en t can be determ ined by either h e ig h t/

volum e-curves (cell (6,2)) o r h eig h t/b asal-area-cu rv es (cell (5,2)). It is com m on p ractice, w hen carrying o u t a local field survey, to sm o o th m easured volum es o f rem aining cro p as a fu n ctio n o f height (this is th e initial fo rm o f the Eichhorn rule, cf. section 4.3). This curve is th en used to estim ate volum e o f stands w here only height has been m easured. A s can be seen fro m cell (6,2) in fig .3-8, this p ro ced u re elim inates th e greater p a rt o f site variatio n . Biilm ann (1943, p .370) utilizes this ad v an tag e to p ro d u ce a h eig h t/v o lu m e-cu rv e fo r yield co n tro l (thinnings an d clear felling) at the estate o f F rijsenborg.

H eigh t/ stem -num ber-curves = R elative distance o f trees

T h in n in g tre a tm e n t can also be determ ined by a h eig h t/stem -n u m b er-cu rv e (cell (4,2)). This curve is interesting, as the m entioned cell describes the m ore an d m ore frequently used v a ria b ­ le: relative distance o f trees. T he cell can disclose w hether this principle has been, o r co u ld have been, used as a treatm ent fu n ctio n fo r th e yield tab le in q u estion. Relative distance o f trees is defined as (see e.g. H andler, 1984, p .363):

R = 100 * V (A rea/N 3) / H 3

W hen the a re a is 1 h ectare it follow s:

(21)

R = 10.000/(VNj*H,) (22)

fro m w hich

N 3 = (1 0 .0 0 0 /R * H 3)2 (23)

F ro m (22), it is seen th a t if stem n u m b er in cell (4,2) is solely a fu n ctio n o f height, then R will also be a function o f height only: R = f(H ).

T he use o f a heig h t/stem -n u m b er-cu rv e (N = f(H )) is th e re fo re identical to using relative dis­

tance as a tre a tm e n t fu n ctio n (R = f(H )). In fig. 14 an d 15 this ob serv atio n is exam ined in detail fo r the 6 yield tables in fig .3-8.

F i g u r e 14. R elative d istan c e o f trees in Vo, as a fu n ctio n o f age fro m seed, fo r 6 yield tab les. T h e sa m e le­

gend as in fig .3-8 is used.

F ig u r 14. Relativ træafstand i %, som funktion a f alder fra frø , f o r 6 bonitetsvise produktionsoversigter.

Der er anvendt samme signatur som i figurerne 3-8.

1 2 3 4 5 6

FAGUS SYLVATICA

QUERCUS ROBUR

PICEA ABIES

FRAXINUS EXCELSIOR

ABIES ALBA

PICEA SITCHENSIS

.

*v.

•k'U ^Ii: Js ^S A

I ^' /1

1 0 2 0 3 0 1 0 2 0 3 0 1 0 2 0 3 0 1 0 2 0 3 0 1 0 2 0 3 0 1 0 2 0 3 0

F i g u r e 1 5. R elative d istan c e o f trees in °/o, as a fu n ctio n o f h eig h t, fo r 6 yield tab les. T h e sam e legend as in fig .3-8 is used.

F ig u r 15. Relativ træafstand i %, som funktion a f højde, f o r 6 bonitetsvise produktionsoversigter. Der er anvendt samme signatur som i figurerne 3-8.

A s can be seen fro m cell (4,2) in fig .3-8, an d also in fig. 14 an d 15, relative distance is n o t used as a tre a tm e n t fu n ctio n in an y o f th e 6 yield tables in q u estion. A t th e sam e tim e, it can be seen, how ever, th a t a curve: R = f(H ), could well have been used as a tre a tm e n t fu n ctio n fo r b o th the silver fir, an d (especially) the sitk a spruce yield tables. F u rth e r it is seen, som ew hat surprisingly, th a t w hen th in n in g tre a tm e n t is described by the use o f relative distan ce, th e tr e a t­

m en t is m ore in d ep en d en t o f site class w hen show n as a fu n ctio n o f age (fig. 14) th a n w hen show n as a fu n ctio n o f height (fig. 15).

T he initial d ro p in relative distan ce, observed in som e o f th e cells in fig. 15, is caused by d if­

ferences in initial spacing a t th e sam e height (see cells (4,2)). T he w ider initial spacing fo r a gi­

ven height, the higher the early level fo r relative distan ce, a n d th erefo re a m o re p ro n o u n ced d ro p in this level will be observed w hen height g row th in th e sta n d begins. This is observed fo r beech, N orw ay spruce an d silver fir.

122

W hen th e curves fo r relative distance are a t m inim um , a certain equalization has ap p eared , elim inating differences caused by initial spacing. D ue to slow er height g ro w th fo r p o o re r site classes, it is to be expected th a t this eq u alizatio n will ap p ear later in tim e (see fig. 14) fo r the p o o r site classes, as initial spacing will be roughly equal regardless o f site class. F o r th e sam e reaso n , no significant initial d ro p is observed fo r the better site classes.

F u rth e r, a fact o ften p o in ted o u t regarding M ø lle r’s yield tables is con firm ed in fig. 14 and .15 (no. 1-4 in the figures), nam ely th a t th in n in g intensities used by M øller increase heavily w ith age (an d height). T he heavy thinnings w ith increasing age observed fo r N orw ay spruce ten d to ap p ro ach a to ta l opening o f th e stand. H ow ever, this treatm en t is seldom follow ed in practice.

These observations w ere already p o in ted o u t by M øller & Nielsen (1953) in their »T esting o f the D anish yield tables o f 1933 fo r beech, o ak a n d N orw ay spruce«. T he significant increase in relative distance fo r heights above 20-25 m observed fo r all site classes in beech, deserves a com m ent how ever. T his increase is p artly due to the fact th a t M ø lle r’s tables fo r beech show a m uch to o low height increm ent fo r o ld er stands (see M øller & Nielsen, 1953, p .9-14). T h ere­

fore th e increase w ith age, observed in fig .14 a n d 15 fo r beech, will n o t be as p ro n o u n ced in reality.

In general, it is seen th a t th e light-dem anding species o ak an d ash are treated w ith thinnings equivalent to a relative distance o f ap p ro x im ately 25% w hen young, increasing to 40-50%

w hen m atu rity is a p p ro a c h e d . Beech a n d N orw ay spruce are treated w ith thinnings equivalent to a relative distance o f betw een 20 a n d 3 0 % , w hile bo th silver fir an d sitk a spruce are treated w ith som ew hat lighter th in n in g grades equivalent to a relative distance o f ap p ro x im ately 20% .

In tab le 4, the relative distances calculated fo r M ø lle r’s yield tables (beech, oak a n d N orw ay spruce) are co m p ared w ith th e m o re com m only used D anish thinning grades. This conversion is carried o u t using figures fo r converting fro m relative distance via relative level o f basal area to th in n in g grade (A : no th in n in g , B: light th in n in g , C: m edium -heavy th in n in g , D: heavy th in ­ ning. In principle, these th in n in g treatm en ts a re determ ined by basal area). Figures fo r this conversion are show n in H andler (1984, p .366, tab le 1). T he conversion is in accordance w ith the equivalent levels rep o rte d fo r beech an d o a k by K litgaard (1987). It m u st be stressed, how ­ ever, th a t the conversion only gives an approxim ate indication, as an exact relationship between relative level o f basal are a an d relative distan ce o f trees does n o t exist.

T a b l e 4. D e scrip tio n o f th e th in n in g in ten sity u sed in M øller’s yield tables fo r b eech, oak a n d N o rw ay spruce (Møller, 1933). T h e relative d istan ce o f trees, c a lcu lated fro m th e yield tab les (figure 14-15), is c o m ­ p a re d ro u g h ly w ith th in n in g g rad es used in D an ish th in n in g experim ents. 1: relative distance o f trees fro m yield ta b le s. 2: c o m p a ra b le th in n in g g rad e, ta k e n fro m ta b le 1 in Handler (1984, p . 366). A : no th in n in g , B:

lig h t th in n in g , C: m ed iu m -h e av y th in n in g , D: heav y th in n in g .

T a b e l 4. Karakteristik a f hugststyrkeniveau anvendt i Møllers produktionsoversigter f o r bøg, eg og rød­

gran (Møller, 1933). En grovere sammenligning mellem den relative træafstand, beregnet fra produktions- oversigterne (figur 14-15), m ed hugststyrke-betegnelserfra danske hugstforsøg. 1: produktionsoversigtens relative træafstand. 2: tilsvarende hugststyrke betegnelse efter tabel 1 hos Handler (1984, p.366). A : ingen tynding, B: svag tynding, C: middel-stærk tynding, D : stæ rk tynding.

B E E C H O A K N O R W A Y S P R U C E

1 2 1 2 1 2

Y o u n g er sta n d s (20-40 years) 20% C -D 25% B-C 20% C-D

O ld er sta n d s (close to m atu rity ) 30% > D 50% > D 25% D

I f we exclude the th in n in g grades used close to age o f ro ta tio n (com m ented u p o n above), it is seen fro m table 4 th a t th e th inning tre a tm e n t used by M øller m ust be ch aracterized as follow s, w hen co m p ared w ith th in n in g p ractice generally used in D en m ark to d ay : weak to m edium (i.e.

appropriate) f o r beech, very weak f o r oa k an d m edium to stron g f o r N o rw a y spruce.

D iam eter / stem -num ber-curves

Cell (4,8) in fig .3-8 show s the diam eter/stem -n u m ber-cu rve. If the n o rm al p ro ced u re o f c o n ­ stru ctio n , described in section 3.1, is follow ed, b o th D an d G will be fixed basic facto rs, a n d N can be derived fro m these as:

N = (4 /jt)* G /D 2 (24)

If cell (5,8) shows th a t basal area is (approxim ately) a function o f D , th en N , according to (24), will also (approxim ately) be a fu n ctio n o f D. T his is seen to apply p artly to beech (fig .3), clearly to oak (fig.4) an d silver fir (fig .7), but n o t a t all to N orw ay spruce. T he observed rela­

tionship is interesting, an d could be used as a n alternative tre a tm e n t fun ctio n .

This has in fact been done by R eineke (1933) in his so-called »stan d density index« (SD I).

SDI is originally conceived purely as an indicator o f stan d density, b u t it could nevertheless be used to regulate stan d density - i.e. as a treatm en t fun ctio n .

C um ulative thinnings

Cells (7,2) a n d (7,3) in fig. 3-8 fu rth e r ch aracterize the effect o f using the tre a tm e n t functions described in section 4.3.

Cell (7,2) show s cum ulative thinnings: A = I V 2, as a fu n ctio n o f height. Fig. 3-7 all show th a t cum ulative volum e th in n ed a t a given height is greater fo r the p o o rer site classes. As also noted in section 4.3, the yield tab le fo r sitka spruce again d iffers to tally from this general tren d (cell (7,2), fig .8), as the o p p o site is th e case fo r this table.

P /A -c u rv e

A m o re condensed d escrip tio n o f th in n in g tre a tm e n t is seen in cell (7,3), th a t show s cum ulative th in n in g s as a fu n ctio n o f to ta l yield a t an y p o in t in tim e, i.e. th e P /A -c u rv e . If, fo r exam ple, cum ulative thinnings consistently acco u n t fo r 50% o f to tal yield, th en th e P /A -c u rv e will be a straig h t line, w ith th e e q u atio n : A = 0.5 * P . F o r each o f th e 6 tables there is a tendency to w ard s a co m m o n P /A -c u rv e fo r all site classes. F ig .5 (N orw ay spruce) a n d fig .8 (sitka spruce) show a P /A -c u rv e alm o st to tally co m m o n to all site classes, w hereas fig .3 (beech), 4 (oak), 6 (ash) an d 7 (silver fir), still show th a t a larger p ro p o rtio n o f to ta l yield is rem oved th ro u g h thinnings fo r p o o re r site classes, th a n fo r b etter site classes. F o r these 4 species we th e re fo re find the heaviest thinnings on th e p o o re r sites.