Growth functions

A system o f age/height-curves is the basis for determ ination o f site class for all yield tables in table 2. For all the yield tables, this age/height system is derived in strict agreement with the ba­

sic data, and without the use o f any growth functions at all (see also Assm ann, 1961, p .156- 158).

From table 2, it is seen that the earliest Danish site-class system was produced for beech by Steen in 1887. (The yield table with 5 site classes, produced by Steen, does in fact not qualify for listing in table 2, as his tables only give the development for remaining crop. They are there­

fore not counted as being acceptable yield tables, cf. section 1.0. They are nevertheless listed in table 2, in order to show, as pointed out above, that they constitute the first Danish site-class system).

P: Total yield

The growth functions, referred to in table 2, are all concerned with the m utual relationship be­

tween site class and the development o f total yield.

The Eichhorn rule, foreign experience

For a given stand, the »Eichhorn rule« states that total yield will be a function o f height only, regardless o f site class. The rule is assumed to apply only within limited regions o f uniform growth conditions, and different relationships between total yield and height will apply to dif­

ferent species: P = f(H).

Eichhorn himself is only partly the originator o f the rule, as he, in his yield table for silver fir (Eichhorn, 1902, p .59 + tab. 5), expresses it in the form : V = f(H). This rule only states that the volume o f the remaining crop is a function o f height. Later Eichhorn shows that the rule al­

so applies to beech and partly to Norway spruce (Eichhorn, 1904, p .46-47). Gehrhardt (1909, p. 118-121) finds th at the rule applies to Norway spruce, Scots pine, silver fir, beech, oak and alder.

With the light thinning intensities used in Germany at the end o f last and the beginning of this century, the volume o f remaining crop constituted the bulk o f total yield. It was therefore natural th at Eichhorn ’s rule was tested and extended also to apply to total yield: P = I I V = f(H).

This »extended Eichhorn rule« (the expression originates from Assm ann, 1955, p .321) was form ulated by Gehrhardt (1921, p. 150) for Scots pine.

M oreover, the rule has been further extended over the last 80 years. By being used and tes­

ted, the rule has gradually been m odified and refined. (Resumés are found in A ssm ann, 1955, p .321-330; Assm ann, 1961, p . 156-174; Pardé, 1961, p .258-260; Mitscherlich, 1963, p . 132- 140; Prodan, 1965, p .600-603; Mitscherlich, 1978, p . 102-103; Kramer, 1988,p .94-95).

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A ssm ann (1961, fig .89, p . 161, 164, ta b . 54, p . 170), M itscherlich (1963, ta b . 31, p. 137, fig.

29, p. 138) an d A ssm ann & Franz (1965, p . 17) sum m arize th a t w ithin th e E u ro p ean area, N o r­

way spruce show s large variations ( + -15-25 % from th e overall m ean) in to tal yield achieved at a given height. T hese differences are p rim arily due to local differences in b asal-area p ro d u c ­ tion, w hereas differences in fo rm facto r have no p a rtic u la r influence (Assm ann, 1961, p. 164).

Schm idt (1973, p .270-271) finds differences o f sim ilar m agnitude fo r Scots pine in E u ro p e.

B raastad (1974, fig .24,p .52) finds differences o f th e sam e m agnitude fo r N orw ay spruce w ith ­ in N o rw ay alone. K e n n e l(\9 1 2 , fig .28,p . 136) dem o n strates v ariatio n s o f + - 3 0 % in to ta l yield at a given height w ithin 24 B avarian sam ple plots fro m th inning experim ents in beech. R eg ard ­ ing th e B ritish » F orest M anagem ent T ab les« , Johnston & B radley (1963, p .219) refer in gene­

ral th a t if volum e p ro d u c tio n fo r a p a rtic u la r stand is determ ined fro m the average relationship betw een height a n d cum ulative volum e p ro d u c tio n alo n e, th en the tru e p ro d u c tio n m ay be as m uch as 50% o u t.

In o rd e r to ta k e som e o f th is v ariatio n in to acco u n t, A ssm ann introduces th e concept o f er- tragsniveau (yield level), describing th e ability o f an individual site to pro d u ce volum e a t a gi­

ven tree height, i.e. a higher o r low er level fo r curves show ing th e relationship: P = f(H ). D if­

ferences in yield level are assum ed to be a result o f v ariatio n s in clim ate, so il condition, p r o v e ­ nance, initial spacing an d thinning intensity (Assm ann, 1961, p . 161,166, 169-174).

W ith in th e E u ro p e a n a re a , tw o m ain clim atically determ ined gradients in yield level can be distinguished fo r N orw ay spruce. P a rtly an east/w e st an d p artly a n o rth /s o u th g rad ien t, gi­

ving th e result th a t w estern a n d so u th ern regions have a higher yield level th a n eastern an d n o r­

th ern regions (Assm ann, 1961, p . 169-171; M itscherlich, 1963, p . 135-138). S chober (1955, esp.

p .53-58) has m ade sim ilar observ atio n s regarding conifers in general, by com paring con d itio n s o f g ro w th an d to ta l yield in G erm any, E ngland an d D enm ark.

T h e n o rth /s o u th grad ien t is prim arily caused by a tem p eratu re-effect, w hereas the east/w e st g rad ien t is a result o f higher h um idity a n d p recip itatio n to w ard s th e west.

T h e w ay in w hich the relatio n sh ip betw een height increm ent a n d basal-area increm ent is a f ­ fected by changing clim atic co n d itio n s, is decisive in determ ining yield level (see Schober, 1955, p .57).

W ith in th e year, height g row th sta rts early a n d o ften term in ates early, w hile diam eter gro w th starts later b u t in re tu rn continues th ro u g h o u t th e g row th season (see L yr, P o lster <6 Fiedler, 1967, p .319-325; M itscherlich, 1975, p. 195-197,206-217; K ram er & K ozlow ski, 1979, p .72-73,92). T he te rm in atio n o f height grow th w ithin th e g row th season is, how ever, d ep en ­ d en t o n w hether th e species belongs to th e »Q uercus-type« o r »P opu lu s-ty p e« (Lyr, P o lster &

Fiedler, 1967, p .319). F o r species belonging to the » Q uercus-type«, height gro w th takes place in th e m o n th s o f M ay -Ju n e, while d iam eter grow th takes place in the m o n th s o f Ju n e-A u - g u st/S e p te m b e r, a t o u r latitu d es. The m a jo rity o f o u r p ro d u c tio n species belongs to this gro u p (Q uercus, F ag u s, P in u s, P icea, A bies etc.). F o r species belonging to the » P o p u lu s-ty p e« , b o th height- a n d d iam eter gro w th ta k e place in the sam e period (M a y /Ju n e -A u g u st/S e p te m b e r).

This g ro u p co n tain s a n u m b er o f ou r less im p o rta n t p ro d u ctio n species (P o p u lu s, B etula, La- rix etc.).

T h e e ast/w est-g rad ien t results from th e fact th a t th e m ore hum id coastal clim ate increases

d iam eter grow th relatively m ore th a n height g ro w th , fo r species belonging to the »Q uercus-ty- pe«. T h e early term in ated height gro w th m ay be sustained on w ater reserves saved u p durin g the w inter p eriod. Increased p recip itatio n an d h u m idity during the grow th season is th erefo re prim arily to the ad v an tag e o f d iam eter grow th.

A t the sam e tim e the w in d -p ro n e coastal clim ate reduces height g row th, w hich, to g eth er w ith th e above-m entioned p recip itatio n effect, causes a higher level o f the h eig h t/to tal-y ie ld - curve in w estern regions.

The n o rth /s o u th g rad ien t is p rim arily a result o f th e extended period o f gro w th in w arm er so u th ern clim ates. D ue to th e early te rm in atio n o f height g row th fo r »Q uercus-type« species, it is especially d iam eter g ro w th th a t is increased by an extended grow th p erio d , which again causes a higher level o f the h eig h t/to tal-y ie ld -cu rv e.

D eviating fro m these m a jo r clim atic g rad ien ts, localities m ay be fo u n d w ith individual yield levels du e to special so il conditions. T he deeper the soil, the b etter the w ater supply available fo r the last p a rt o f the grow ing season. This especially increases d iam eter g ro w th , an d th e re ­ fore results in a higher yield level. A ssm ann (1961, p . 162,167,173) describes specific exam ples o f this (see description o f D anish exam ples later in the text).

T he influence o f differences in thinning intensity (A ssm ann, 1955, p .327; Assm ann, 1961, p. 164-168) is prim arily caused by th e purely statistic change o f m ean height com bined w ith low th inning. This effect m ay be p artly elim inated by using d o m in an t height in the expression P = f(H ). T o this is added the influence o f th in n in g intensity on volum e increm ent. This influence m ay be b o th positive an d negative depending on w here in the range: m axim um -, o p tim u m - an d critical level o f basal a re a th e stan d is situ ated (A ssm an n , 1961, p .222 an d foil.). It follow s th a t heavy thinning m ay result in a higher o r low er level o f the h eig h t/to tal-y ie ld -cu rv e, as the height effect an d th e volum e-increm ent effect m ay either enhance o r oppose each o th er.

T he yield level - i.e. th e basal-area p ro d u c tio n p o ten tial - can in any given region be m easu ­ red in u n th in n e d stan d s, w hereby we achieve a co rrectio n o f local yield (A ssm ann, 1955, p .327- 329; A ssm ann, 1961, p . 168,173; H am ilton & Christie, 1971, p .7-8).

Several a u th o rs find th a t y ie ld level varies system atically with site class, o fte n in such a w ay th a t th e low est site class has the highest yield level (see e.g. P rodan, 1965, p .602 reg ard in g Scots pine a n d o ak ; Schober, 1971, p .28 regarding beech; Schm idt, 1973, p .270-271 regarding Scots pine). T here ap p ears to be a tendency indicating th a t this applies to broadleaves and the m ore light-dem anding conifers (see fig .3, 4, 6, cell (3,2)), w hile th e opposite is th e case fo r th e m ore sh ad e-to leran t conifers (see fig .5 a n d 8, cell (3,2)). A s an exam ple, A ssm ann & F ran z’ yield table fo r N orw ay spruce (1965, p .29) show s higher yield levels fo r the b etter site classes. (In fig .7, how ever, the o p p o site tendency is seen fo r silver fir. F u rth e r, A ssm ann (1961, p . 167) re­

fers to exam ples o f b o th higher a n d low er yield levels fo r th e b etter site classes fo r N orw ay spruce).

As discussed ab o v e, m any facto rs cause differences in yield level. T he to ta l v ariatio n in yield level m ay be divided in to th e follow ing co m p o n en ts (see A ssm ann & Franz, 1965, p. 17-20,28- 29; Schm idt, 1973, p.269; K ram er, 1988, p .4 9 ,94-95, 121-125):

W ithin a specific region th e average y ie ld level (m ittlere ertragsniveau) d enotes th e average

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curve fo r P = f(H ). In this co n tex t, a region indicates an area sufficiently u n ifo rm to ju stify p ro d u c tio n o f a yield tab le w ith several site classes. G eneral y ie ld level (allgem eine ertragsni- veau) denotes differences in yield level betw een site classes. T he concept o f general yield level is thus equivalent to fo rm u latin g to ta l yield as a fu n ctio n o f b o th height an d age: P = f(H ,T ).

F inally, th e concept specific y ield level (spezielle ertragsniveau) covers differences in yield level within an individual site class.

A ssm ann & Franz (1965, p. 17) are th e first to in c o rp o ra te 3 specific yield levels (»unteres-, m ittleres-, oberes-ertragsniveau«) in th e ir yield table fo r N orw ay spruce in B avaria. A cco r­

dingly, they have p ro d u ced 3 yield tables fo r each site class, co rresponding to one yield table fo r each o f the specific yield levels. T he in tro d u c tio n o f specific yield level is equivalent to fo r­

m ulating to ta l yield as a fu n ctio n o f height, age a n d th e specific level: P = f(H ,T ,L ev ). This principle is illustrated in figure 9.

H

F i g u r e 9. Illu stra tio n o f th e c o n cep t o f average, general a n d specific yield level. S ig n atu re : A verage yield level: p u n c tu a te d cu rv e. G en eral yield level: fully d raw n curves. Specific yield level: d o tte d curves. F o r f u r­

th er e x p la n a tio n , see p . 110-1 I I .

F ig u r 9. Illustration a f begreberne gennemsnitligt, generelt og specielt ertragsniveau. Signatur: Gennem­

snitligt ertragsniveau: stiplet. Generelt ertragsniveau: fu ld t optrukket. Specielt ertragsniveau: prikket. For yderligere forklaring, se teksten p . 110-1 II.

F igure 9 show s h eig h t/to tal-y ield -cu rv es fo r 3 site classes fro m a (fictive) yield tab le. T he average y ie ld level is show n by th e p u n ctu ated curve.

F o r each site class an u p p er (3) an d low er (1) specific y ie ld level is seen. T he specific level 2

( = average) is identical to th e general y ie ld level fo r the individual site class. GeneraI yield le­

vels are au to m atically included in A ssm ann & F ran z’ (1965) yield table. W hich o f the 3 specific levels to be used m u st be d eterm in ed , as form erly m en tio n ed , fro m long-term m easurem ents o f to tal yield in u n th in n ed stands o r in stands w ith so-called o p tim u m basal area (see K ram er,

1988, p .9 4 ,121-122).

Sim ilarly, H am ilton & Christie (1971, p .4-5) use 3 specific yield levels (a ,b ,c = p ro d u ctio n classes) in their yield tables fo r a n u m b er o f species grow n in th e U .K . These tables, how ever, show n o difference in yield level betw een site classes. A ccordingly, general yield level is co m ­ m on to each individual species, w ith the exception, alth o u g h , o f oak an d beech. T he a u th o rs em phasize th a t th is sim plification will n o t apply to higher ages, when height g row th begins to stag n ate. F o r coniferous species the tables stop b efo re this critical p o in t is reached, w hereas this is n o t the case fo r th e oak a n d beech tables (H am ilton & Christie, 1971, p. 112-113; John­

ston, G rayson & B radley, 1967, p .203-207).'

B raastad (1974, p .49) uses 3 specific yield levels fo r N orw ay spruce in N orw ay (»øvre-, m idiere-, nedre- p ro d u k sjo n sn iv å« ). L em b ck e et al. (1975, p .5) uses 3 specific yield levels fo r Scots p in e in E ast G erm any. T o ta l yield a t the u p p er level is 10% above average level a t all ages, w hereas th e low er level lies 10% below . F u rth e rm o re , C arbonnier (1975, p .20-21,27- 28,33) uses 3 specific yield levels in a yield tab le fo r oak in Sw eden. In c o n tra st to the yield ta b ­ les so fa r discussed, Carbonnier determ ines this yield level directly from th e silt an d clay fra c ­ tion ( < 0 .0 6 m m ), w hich ap p ears as an independent v ariable in th e increm ent fu n ctio n .

T he in tro d u cio n o f 3 yield level co m p o n en ts (average, general an d specific) is obviously still a sim plification o f a m ore com plex reality. It is, how ever, a w ell-justified ad d itio n to the sim ple Eichhorn rule: P = f(H ).

F o r an y given site class, a high (specific) yield level expresses above-average g ro w th , w hereas a low (specific) yield level expresses below -average g row th. If, on th e o th er h an d , differences in yield level were conceived as v ariatio n s a ro u n d th e average level, we w ould o fte n find th a t the p o o rest site classes co rresp o n d to th e highest yield levels, a n d vica versa (see p. 109). U sing this co n cep t, a high yield level could in effect be equivalent to inferior g ro w th , w hich is illogical.

If we do n o t distinguish betw een general a n d specific yield level, effects o f h ig h /lo w height grow th a n d h ig h /lo w b asal-area g ro w th will be c o n fo u n d ed . In this case, a high yield level could solely be a result o f a depression in height gro w th (e.g. caused by w ind-w ear) fo r a given basal-area p ro d u c tio n . This co n fu sio n will n o t be possible w hen to ta l v ariatio n in yield level is divided in to the above-described 3 co m p o n en ts. W ithin this concept, a depression in height g row th will result in a se p a ra te g eneral yield level (i.e. a d ifferen t site class curve), a n d n o t in a higher specific yield level. T he in tro d u c tio n o f 3 yield level co m ponents th erefo re ap p ears well ju stified .

T he »extended Eichhorn rule« is given the follow ing form : P = I I V = f(H ), w hich co rres­

ponds to the average yield level in th e above-described term inology. In stead o f a single fu n c­

tion fo r each species, we find a fam ily o f h e ig h t/to tal-y ie ld -cu rv es, each curve equivalent to

the general yield level fo r the individual site class. Finally, a specific yield level is a d d ed to the general yield level (see fig. 9). G eneral yield level is th erefo re the result o f differences in grow th conditions th a t also express them selves in site class. Specific yield level, on the o th e r h an d , is the result o f differences in g ro w th co n d itio n s th a t d o n o t express them selves in site class.

D ifferences in general y ie ld level will first an d fo rem o st be caused by the above-m entioned m a jo r clim atic g radients as well as sim ilar gradients in soil co n d itio n . F actors th a t affect the general yield levels will obviously also a ffe c t the average y ie ld level. T he specific y ie ld level will, o n th e o th e r h an d , be determ ined by m ore local v ariations in clim ate a n d soil co n d itio n s, as well as p rovenance, establishm ent intensity an d th in n in g treatm en t.

The Eichhorn rule, Danish experience

A n u m b er o f D anish a u th o rs have observed stands o r localities with highly deviating y ie ld le­

vels. As to the causes, hypotheses sim ilar to th e above have been suggested, i.e. differences in clim ate, soil c o n d itio n , w ater supply etc. (see Løvengreen, 1951b, p . 361 regarding N orw ay spruce; L undberg, 1954, p .233 regarding beech; B ryndum , 1957, p .382 regarding o ak ; H enrik­

sen, 1955, p .572-573 regarding conifers in general; H enriksen, 1956, p .352-356; H enriksen, 1958b, p .29,213-218, b o th regarding sitk a spruce; H enriksen, 1958a, p .499 reg ard in g sitka spruce, silver fir an d beech).

H ow ever, no Danish y ie ld tables m ake use o f differen t (specific) y ie ld levels, alth o u g h su b ­ stan tial differences in »ertragsniveau« h ave been fo u n d fo r a n u m b er o f species w ithin the li­

m ited D anish region, as m entioned ab o v e. Jakobsen (table 2, n o . 10, 1976, p .320,325), M øller M adsen (no. 11, 1989), M agnussen (no. 16, 1983, p .227) an d Elingård-Larsen & Jensen (no. 17, 1985, p .254) all derive a h eig h t/to tal-y ie ld -cu rv e com m on to all site classes, an d thereb y use the Eichhorn rule in its m o st sim ple fo rm .

F o r the co n stru ctio n o f the yield tab les fo r beech, o ak an d N orw ay spruce, M øller (no. 12, 13, 14, 1933) em ploys E ich h orn ’s rule in p a rt. T he achieved to tal yield a t th e reference age (for beech = 100 years, oak = 120 years, N o rw ay spruce = 50 years) is assum ed to be a fu n ctio n o f height alone (M øller, 1933, p .463,466-467,541-542). These heig h t/to tal-y ield -cu rv es are only used to determ ine th e accu m u lated p ro d u c tio n fo r each site class a t th e reference age, w hereas the Eichhorn rule is n o t em ployed fo r d istrib u tin g this p ro d u c tio n over tim e (see th e descrip­

tion in table 2, nos. 12,13 a n d 14). A ccordingly, it can be seen in fig .3 ,4 an d 5 (cell (3,2)), th a t the Eichhorn rule does n o t apply to th e D anish yield tables fo r beech an d o a k , w hereas it a p ­ plies ap p ro x im ately to N orw ay spruce.

T h e Eichhorn ru le in its sim ple fo rm : P = f(H ), is fu rth e r used a n d tested in several D anish p u b lic a tio n s on th e to p ic o f g ro w th a n d yield.

Henriksen (1958b, p.27-29) h as tested th e v a lid ity o f the Eichhorn rule o n his sitk a spruce yield ta b le . H e fin d s th a t th e rule does not a p p ly to sitk a sp ru c e u n d e r D anish c o n d itio n s, as th e best site classes have h ad th e highest to ta l yield a t an y given height. A t a height o f 15 m eters, site class 1 h as p ro d u c e d 385 m \ w here­

as site class 4 h as on ly p ro d u c e d 297 m 3, i.e. a lm o st 90 m 3 less. H ow ever, th e relative differen ce betw een th e site classes decreases fo r increasing heights. It th e re fo re follow s th a t th e ru le applies so m e w h at b e tte r at g reater heights.

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spruce do es n o t, in g en eral, follow th e Eichhorn rule. T h e divergencies fro m th e Eichhorn rule, observed in the D an ish m a te ria l, m ay very well arise fro m im b alan ces in h eren t in the basic m a te ria l. The test o f th e Eichhorn rule fo r D anish sitk a sp ru ce can be seen in fig .8, cell (3,2). In this g ra p h th e d iscrepancies a p p e a r to be q u ite m in im al, b u t th e d im in u tiv e scale m u st be ta k e n in to c o n sid e ra tio n . A t 15 m e te rs’ h eig h t, the d ifferen ce betw een th e highest a n d low est site class is, as m e n tio n e d , 90 m 3.

I f we o b serv e cell (3,2) in all th e m atric es (fig .3-8), it is seen th a t only MøUer’s yield tab le fo r N o rw ay spruce show s reaso n a b le ag reem en t w ith th e Eichhorn rule.

A test o f th e Eichhorn rule fo r th e N o rw ay sp ru ce yield ta b le is show n in ta b le 3.

T a b l e 3. T esting th e ap p licab ility o f th e Eichhorn ru le o n M øller’s yield ta b le fo r N o rw ay sp ru ce (1933,

T a b l e 3. T esting th e ap p licab ility o f th e Eichhorn ru le o n M øller’s yield ta b le fo r N o rw ay sp ru ce (1933,

In document DET FORSTLIGE FORSØGSVÆSEN I DANMARK (Sider 38-48)