Reprinted from
Forest Ecology and Management
Forest Ecology and Management 120 (1999) 59-76
Simulation of tree and stand development under different environmental conditions with a physiologically based model R. Grote":", M. Erhard b "Institute for Forest Growth Research. University of Munich. Am Hochanger 13, D·85354 Freising. Germany f> Porsdam Institute fo r Climate Impact Research, PO . Box 60 12 03, D-14412 Potsdam, Germany Received 15 October 1997; accepted 28 October 1998
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Forest Ecology and Management
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ELSEVIER
Forest Ecology and Management C O ( 999) 59-76
Simulation of tree and stand development under different environmental conditions with a physiologically based model . R. Grate a.*. M. Erhardb "Institute fo r FO n:Sl Growth Resea rch. University of Munich. A.m Hochunger 13. D-8535.J Freising. Germany "Potsdam Instill/le f o r Climate Impact Research. P O. Box 60 12 03, D-I-U12 Potsdam. Germany
Received 15 October 199i ; accepted 28 October 1998
Abstract A simulation appr oach is used to describ e annual tree growth and tree mortality fro m the output of a physiologically based model (FO RSA.'J'A ). Heigh t and diameter growth are calculated directly from the amount of carbon allocated to sapwood by considering I n optimum height/diameter rati o. which depends on stand density. Tree mortality is defined by means of a relation between ner primary production and carbon loss due to compartment senescence. Thus. all responses to environment al conditions considered in the physiologic al pan of the model are implicitly considered in the stand development description. The dynamic simulation of stand pro pe rties . on the oth er hand. is required to apply the physiological based process description [0 long-term assessments. The model is used to descri be height and diameter develop ment of three Scots pine (Pinus sylvestris L. ) stands in eastern Germany whi ch are expos ed to different levels of nitroge n deposition and SO::: air pollution. Resu lts are compared with tree ring analy sis covering a period of 27 years. For further evaluation. the model is initialised with forest inventory data of 288 pine stands and is run over 23 years using daily weather and deposition data as well as fertilisation information as input. The results are co mpared [Q data fr om a seco nd inventory of [he same stands. This comparison is conducted separately for regions exposed [Q high and low deposi tion. The model represe nts annual height and diame ter development at two of the three selected sites . With respect to the third site. considerable distu rbunces in the ear ly years of stand development are assumed to be responsible for the unusual growth trend. The region al evaluatio n of [he mode l yields correlation coefficients with forest inventory data between 0.57 and 0.86. with a generally bette r tit on diameter and sremw ood volume than height. The approach demonstrates the uncertainty of estimations which are based on investigations at only few sites. and is discussed as a possible method for regional assessment of forest de velopment unde r environmental change. 1999 Elsevier Science B.Y. All rights reserved.
r
Keyw ords: Environment al chan ge: Nitrogen: Air poll ution; Tree growth: Mortali ty: Modelling
1. Introduction
"Correspond ing autho r. Te!.: ---+9 - ;~16 1 -i1--l.i l l: lux: .-.....I.~ . x lnl · -;I-..+i: I: e-ma il: Ruedige r.gr otets' lrz. uni -m uenchen.dc
(H7.'-: ·112 7/9l.,l/'S -
~ t.:e fro m matter
1_
r !l:SO .~ i:'i · 11 ': 7 1l)S I I) ()511 · :i
The unce rta inty in futur e cl ima te co nditions and atmo sp heric depos ition increases the demand for upprop n ute too ls that are able to evaluate the effe ct
19S19 Elsevier Sc ience B.V. All rights reserved.
oD
1l"'S - 1i-S Steniwood votw ne "' :-.I- S - :'1 - 5
( /1/"
--
--
17.0 18.3 18.9 19.1
"
--
_ . ~
1.9
102
30.7 38.2 39.3 .'..1 .:\
90 9 102
ha -I)
- N- 5
110.6 138.5 t3 1.3
- ~- S
1 ~ 1. -I
30.0
36.9 19.5 »r. »
153.7 19-1.-1 195.3 : I l.l
87
-:\I' : teru iixed more than twice Juring: the inve stigat ion period: ~ S ; average annual SO: co ncenrrano n or' 19Y} above 75 pph.
62
R. Grate. M. Erhard /Forest Eco logy
Table 2 Site and stand dat a of the three intens ively investigated sta nds Neuglobsow Age 11993) Average heigh t (m) Average diameter at 1.3 ill (cm) Stemwood volume (m:-) Stem number (ha- I) Soil water capacity (SiC ) Nitrogen content of current needles (%) Estimated fertil isation from 197 0-1985 (kg N ha - I) Annual ave rage SO::, air conce ntr atio n 1989 (umol ill - .' ) Annual average 50 2 air concentrati on 1994 (umol m- ~ )
Tauru 41 18.0 20.6
60 20. 1 21.0 339 104 3
852
125
215
1.43
242
1.80
Rosa 64 16.0 20 .7 208 788 170 2.10
200
lOO
900
50
86
130
12
34
57
site. Neuglobsow. More detailed data concerning the sites and their history are pre sented in Table 2 and are documented in HUlll et a!. (1995). Tree ring analyses for mod el evaluation were performed in 1995 on stem discs of five harvested trees from each stand , with each of the five trees belonging to a different diameter class (10- 15, 15-20, 20-25, 25-30, >30 cm). The results were weighted by the stem number within each class at each site. Daily weather records from 1967 through 1993 were obtained from the weather stations Neuglobsow (for Neuglobsow) and Wittenberg (for Rosa and Taura) of the German weather service . Deposition was estimated by the methods described above. Initial stand data for the long-term simulati on of the three inten sively investigated sites were not available. Thu s. they were estimated from stand age with empirically developed functions of height , diameter and stand volume. based on the forest inventory data of a representative forest district. The soil data were initiali sed as measured in 1994. but total nitrogen content was reduced by the amount of total fertilisation at the specific site. Additional gains from nitrogen deposition or losses. for example. due to percolation were not considered, No information about thinning in the simulated stands were available except genera l management rules for foresters. Thus. a thinning procedure is implemented in the stand growth model which mimic s the conventional forest practice by decreasing tree number at intervals which depend on the height
Gil d
Mana gement 120 (1999) 5 9-76
growth of the stand. The intensity of a thinning is set to decrease with stand age. Fertilisation. which generally had been applied as urea (CO(NH, J,l. is considered by the model as additional deposition of 100 kg N in the form of ammonium. equally distributed throughout the year of application . 2.3. Model description In the modelling approa ch it is assumed that the stand is horizontally homogeneous and that stand processes can be described by means of the average stem. The mode l does not account for differences in tree individual s and is thus only suitable for uniform forest plantations. Since not all trees are of the same size even in a plantation. the stem number calculated by the model from stand volume is only virtual and does not intend to represent the actual number of trees . Since the physiologi cal part of the model is explained in two separate papers (Grote, 1998; Grote and Suckow, 1998). this part of the model is only roughly explained. Nevertheless, some basic or new feature s of the model are given in the Appendix A to make the rationale easier to understand. The stand development is described in mor e detail, including the presentation of the parameters used in the equation (Table 3).
Table 3 Stan d mod el parameters Value
!'Jame
M eaning
.6.H ri "
He ight growth interval after fir st 1.8 thinning app licat io n Max dia met er 0.4 0.45 Wood density Final bran ch fracti on on sapwood 0.14 Coarse roo t fr action on sapw ood 0 .2 Th inni ng int ensi ty par ameter om Biomass relation of average om harve sted tr ee to av era ge tree He ight at which firs t thinning 13 is app lied Expo nential par ame ter 10 Crown/diameter ra tio 13.3 Max height diameter ratio 130 40 M in he ight diam ete r ratio Slope of tre e mortali ty fun ction 0.3
l·
D 13 m ~ x
DEN S FBRA min FCRT FPS N " FfHIN" H m i ll
a
KB QC DD QHDm"x QHD min SLO_V
Unit m
m kg dm":'
m
" Reg ional eval uation, in ye ar-to-year eva luati on adjusted accord ing to the spe cific stand .
R. Grate..'lit. Erha rd / Forest Ecology and Management 1]0 ( 1999 J 59-76
2.4. Phvsiological components The physio logic al model sep ar ately describes the ca nopy light cl imat e acc ording to the Beer-Lambert law for diffuse an d dire ct rad iatio n in a num ber of canopy layers (Spitters et al. , 19 86). The es tim at io n of net primary productio n is taken from the FOR GRO model (Mo hren. 1987 : Mohre n et al.. 199 3). wh ic h calc ulates gross ph o to synthesis fr om an exponential dependency on light (S pitters. 1986) and maintenance resp ira tion fro m te m pe ra ture and m ineral co ntent of each organ. Maxim um phot osynt hesis is limited by the nitrogen co nte nt o f the folia ge (Aber et al., 1996) as we ll as CO : and SO: co nce ntra tio ns (Mohren et al., 1992). Temperature affec ts the C O: -c ompensat ion point and wa ter stress de vel opment in dependence on potential eva po ratio n (Monteith, 1965) relati ve to maximum transpiratio n. T he latter is calculated explicitly fro m soil wate r cont e nt. co ns idering roo t bio mass and distributio n. grou nd vege ta tio n competiti on . and sapwood wate r storage (G ra te and Suckow. 1998) . Car bon and nitroge n all ocation to fo lia ge (whic h is further divided by fo liage age classe s ). woody c o mpartme nts (sapwood. heartwoo d. branch es and co arse roo ts). rege nerative tissue. fine roots. and reserve carbohy drates is determined on dail y time steps usi ng a so urce/sinkrela ted approach. The sink stre ngth of co m partments is basically defi ned ac c ording to the princi pl e of func tional balanc e by their re la tionship to fol ia ge biornass, but this relation shi p is allo wed to vary acc ording to water and ni trogen supply (Grote, 1998) . New foliage growth is su pplied fro m the reserv e po o l wi th depende nce o n tem perature sum. Fol iage mo rtali ty is calculated fro m the re lati on ship between ne t carbon gain and maintenanc e resp ira tio n . Fine root mo rta lity increases with dec reasing so il water co ntent. Two pathways are considered o n nitro gen upt ak e . So il nitrogen up take depends on water up take and the concentratio n of diffe re nt nitrogen species in the soil sol ut ion. Canop y uptake is estimated from deposi tion data (Grote, 1998 ). Soil proc esses are de scribed with a mec hanis tic su bmodel based o n an agricultural mod el (Karts c hall et al.. 1990 : Suckow, 1986). 2.5. Height and dia meter grow th
hectare (N) and the annual sum of sapwood grow th of the stand (G SA P) . simulated by the physio lo gica l parr of the mode l,
Gm
GSA P =N x
is c alc ula ted fro m (virtual) tree number per
( I - FBRA - FCRT )
(1 )
It is ass um ed that the coarse root fraction (FCRT) does no t change in time. whereas the branch fraction (FB R s\ ) increases with stem diame ter at breast height (D 13) in rela tion to the pararneterized max imum diame ter (D l3 m" , ) . minimu m branch traction (FERA mi , ) . and an expone ntial param eter (KB) (equatio n fro m Bos se!. 1994 ). FBRA = FBRAmi, -'- (1 - FBRA mi, )e (- KBiDI3 013=, ))
(2) In the next step. the new diameter at breast he ight and tree height (H) are calcu la ted from the incr ease in stemwood biomass (G STE) ' Therefore. the co ntributions of diameter and height increment (dDO and dH) to ste m incr e ment are differe ntia ted with respect to tim e (fo r eq uation the ory see Bossel, (99 4): CMV x d(DO" x H ) C STE
=
dl
= CM V x D-, x ( 2 x HP DO x d + DO x dH ) ( 0, ) with 7f
CM V = DENS x FORM x -
-I
(-I)
Wi th DENS being a parame ter for wood den sity and FORM deno ting the re latio n between a cyli nder derived from DO and H and the actual stem form . In contras t to Bosse!. we assume the tree stem as a cone . In this case. the fo rm parameter is always onethird and DO refers to the base diameter instead of the diame ter at breas t height. Fro m Eq. (3). the max imu m diame ter incre ase ca n be o btai ned . if height gro wth is assumed zero: GSTE
GDO ma, = 2 x C:'vIV x H x DO
15)
On the other hand. the max imum height growth ca n be de rived by ass uming no dia meter growth :
First. the annual .ste m wood increase pe r hec tare 1G'TE)
63
G ITE
CH",",
= C:"IV x
DO'
16 )
R. Grotc. M. E rhard / Forest Ecology and Managem ent 120 (1999) 59-76
Without a change in the relati on between diameter and height. Eq. (3) yields the following description of diameter growth: GDO =
GSTE 3x CM Vx H x D O
(7)
However , if the deviation between height and diameter growth should be described in dependen ce on environmental conditions, Eq. (7 ) can be transformed to include a variable height/diameter relationship (QHD",). . (
G STE
GDO = mm GDOm", x 3 x CMV x QHD ", x DO'
)
(8)
QHD , ac shifts between parameterized boarders (QHD min and QHD m,,) in dependence on stand density, which is descri bed by the crown area index (CA!). CAl stands for the fracti on of crown-covered area in relation to total stand area and is derived from the stem numbe r, average diameter and the parameterized ratio between breast height diam eter and crown diam eter (QCDD) . QHD,.,,= min (QHD m" ,
QHD min
+ (QHD n" , - QHDmin)CAI ) ") IT N CAl = (DJ 3 x QCDD t x .4 x 10000
(9) (10)
Due to the assumptions made about the stem form , the new height and tbe diameter at breast height can be simply calculat ed from the diameter increment and the old dimensions. H =H+GH",,, ( 1 - - GXDO) - - G x DOmax.
(11)
VIT =
sented in depend ence to changing environmental con-
ditions. How ever, it is assumed that the relationship between base diameter and stem volume is constant (1/3), what is actually not the case. In yield tables, a set of empiricall y found form factors is used to describe tree volume in dep endence on diameter at breast height. Compared to estimations based on these numbers the model yield s almost 20% less stand volume if the height, diameter and stem number of the investigated stands are used. However, since the actual form factor s of the sample d tree s have been found to be considerably small er than those in the yield tables (Wenk , unpublished data) , the estimated volume seem s to be only about 10% small er than the actual one - the same magni tude of error as produced by the yield table meth od. This error is not constant but depends on the actual tree form and decreases with decreasing height/diameter relationship as well as increasing diameter. Sin ce stand volume and not tree number is used as an initial value, virtual tree number is somewhat increased by this error and thu s there is only a small effect on stand volume increase. Nevertheless, in young stands with small dia meter and relati vely large height, the error leads to a con siderable different tree mortality, Thi s is why no stands younger than 40 years are uses in this study. 2.6. Tree mortality and harv esting A vitalit y inde x (VIT) is introduced to characterise tree health. It is calculated by dividin g net primary production (POOL) by total annual compartment mortality (M, foliage = l\TDL, fine roo ts = FRT, coarse roots = CRT, branches = BRA, regenerative tissue = RE N) including core wood formati on (M S A P) and exudation losse s (G EXS ) ' :S POOL
:S (M N DL + M FRT + M sA P + MCRT
DJ3 = (G x DO+DO) x
(H - I 3) H '
(1 2 )
The repre sentation of tree stems as co ne-shaped is somewhat unconventional in forest biometry. The model has the advantag e that a continuous chang e in height and diameter development can be repre-
+ M BRA
+ M R E ,\
+ GEXS )
(13)
By mean s of VIT and the slope parameter SLO_V, the probability for natural tree mortality (FrOT) is calculated. FrOT -- 1 _ VIT SLO - v ,
if VIT < I
FrOT = O.
ifVIT :::: I
(14)
65
R. G rate. M, Erhard l Forest Ecolo gy and Ma nag ement 120 ( 1999) 59- ;"6
(
I/ ' INITIALISATION
I
I
Ini~ial
S~and
Da~a
\
(essent:.ia~)
Secondary S'tan d Da'ta
, ( C r o w n base ne uarn: , Canopy a l.o a ur- e , Ht3 ~gl1T: ! and D~am9T:er 01" \"'''-o urr er- en t: Tree c~assesJ!
!
TK,; (A6)
if L:.6.DVS m", 2: or DVSmm(t) DVSmm(t - I )
ilDVS mm = O.
:s
UMAX
~
) (A 3 )
FRT UMAXFRT + UMAXFRT_v
UMAX FRT• maximum fine root uptake of trees (derived from fine root biomass and specific conduc-
.6.DVS m", = min (O.05, Kmm x (DVSmo, (t) - (DVSnmt )(t - 1) )).
if DAY
< 364
R. Grate. Jf Erltard /Fore st Ecology ami J/anagemenr 120 (1999) 59- 76
~DVS "" " =
I - L~D VS mo, '
otherwis e
DVSmm =
QRA - QRA,m" I _ QRA
if QR.A mi, < !
(A7)
nlln
DVSmm = O.
if QRAmm 2:
(AS)
~D V S """ . frac tio n of da ily fo li age morta lity : DVS""". develo pm ent state of fol iage mortality: DAY. day of the year : K moc• curv e para meter: QR.",,-. ratio between daily resp iratio n and net assimilation: QR.""-min- smallest QRA of the year. The share of fine roots that die during a day develops between a parame terised max im um and minimum value acco rding to the water-stre ss factor. which is calculated fro m the amou nt of water in a particular soil layer relative to the wa ter co ntent at field capacity. F'vl FRT
= T a rn,., - (T Om:!., - TO"'i' )
X
RWmer (A9 )
PvIFRT. fractio n of fine root morta lity in each soil layer: TO:11U.'" maximum daily turn ove r: TO m i n , minimum daily turno ver: R\V nw r ' wa ter-stress factor. Canopy nitrogen uptake is calculated fro m daily :--;0, and ~11 .' field de position rates ass uming that the deposition at fores ts is so mew hat increased co mpared to the field and tha t a net uptak e of nitroge n can only occur if foliage nitrog en conce ntr ation is below a certain threshold. Fu rthermore. cano py up take is limited by a maximum up take rate which is estimated tram leaf area index and water stress.
l:~, . canopy up take of nitrogen (kg ha - I): UN,,,,,. da ily maximum upt ak e of nitro gen (kg m - ' I: LA!. kat" area index: R\V~to, water-stress fac tor. reduc ing stomatal cond uc tivity: CNF. nitro gen concentration at foliage: CNF"p,. optimum value for CNF (calculated from pararneterised maximum and critical values): CNF"i ' critical value for C:-1F: DEP v " . dailv deposition of NO , (kg ha - I I: DEP " H.'. dail'y deposirion or" ):"H , I k2: h:.l- I ) : FDEP. facto r increasina ~" !d deposition I:alculated tro rn leaf area and stand J t:;lsity ).
i5
Refer ences Abet. l .D.. Reich. P.B.. Gouid en. L.. 1996, Extra polating leaf CO: exchang e to the canopy: a ge ne ralized model of forest photosy nthesis compared wi th measurements by eddy correlation. Oecologia 106. 257- 265. Anonymus. 1997, SAi'iA - Wissenschaftlicbes Begleitprcgramrn zur San ierung der Atm csp hdre ube r den neuen Bundeslandem . BMB F. Bcn n, Bassow. S.L.. Ford. E,D ,. Kiester, A..R.. 1990. A crit ique of ca rbo nbased tree growth models. In: Dixon. R.K.. Meldahl. R,S.. Ruark. G,A.. Warre n. W,G . t lids .). Process modelin g of fores t growth responses to e nviro nme nta l stress . Timb er Press. Portla nd, OR. USA. pp. ; 0-; 6. Bergmann. l· H.. Flohr. \V.. 1989. Die Eutrophierung unse rer Wiilder durch Stic ksto tf und ihr e Konseq ue nzen fur die Kiefe m wirtschaft . Soz. Fc rstwi rrschart 39. 373-376. Bossel. H.. 1994. TREED'0 f 3 Forest Simulation Model. Forsch ungszentrum Waldokosyste me . B/3 5. Universitar Gcningen. Gdt tinge n. 118 pp. Bowes. :\LD.. Scdjo. R.A . Impacts and responses to climate cha nge in forests of the i\-tL'\JK regi on. Clim atic Chan ge 24{ 1-2). 1993. 63-82, Chen. C.W.. Tsai. WT. Gomez. L E.. 1994. Modeling responses of Ponderosa pine to interacting stresses of ozone and droug ht. For. Sd. J OI2). 267-288. Cons table. J.V H., Taylor, G.EJ .. Lauren ce. l A.. Weber. I,A.. 1996. Clima tic change effects on the physiology and growth of Pinus ponderosa: expectations fro m simulation mode ling. Ca n, r. For, Res. 26. 131 5-13 25. Cropper, W,PJ .. Gholz. H.L.. 1993. Simulation of the carbon dynamics of a Florida slash pine plantation. Ecol. Modell. 66. 231- 2J9. Fosberg, :\1.A.. 1990, Global change - a cha llenge to modeli ng. In: Dixc n. R.K.. Meldah l. R.S.. Ruar k. G.A.. Warren. W.G. (Eds.). Process modeling of forest gro wth responses to environme ntal stress, Timber Press. Port land . OR, pp. 3- 7. Frien d. ,.1.,D.. Stevens. A,K.. Knox. R.G.. Cannell. ~tG.R.. 199i . A proce ss-based. te rres tria l bio sphe re model of ec osystem dynamics (Hybrid \'3 ,0). Eeol. Modell. 95. 249-287. Gro re. R.. 1998. Integrati ng dy namic mo rphological properti es into forest growth rnodeling Il . Alloca tio n and mortali ty. For, EeoL Man age. Il l. 193- 110. Gro re. R.. Suckow, E. 1998 , Integ rati ng dynamic morp hological properties into fores t growth mod eling L Effects on water balance and gJ.S exch ange , For, Ecol. Mana ge, 112. 101-119. Hunt. E,R.. Martin. F.e.. Running. S.W.. 1991. Simulating the effects of climatic variation on stem carb on accumulation of a ponderosa pine stan d: comparison with annual growth increme nt da ta, In: Kau fmann. :\i.R. . Lands berg. Lj . t Eds. ). Advancing Toward Clos ed Model s of Forest Ecosyste ms. Heron. Victoria. Canada. pp. 161-171. Hunl. R,E . Bellmann. K.. Se iler. W. IEds.l. 1995. Atmos phdrensunierun g und Wuldokcsvstemc . Umweltwissenschafren. .1-, Blottner V~ rl a g . Taunu sstein. p. 238, Kahn. \ 1.. lYo) , Quasikau saie .\lt1Jcllicru ng des Standort-Lcisrungs-Be zugcs als Vorausset zun g zum Aufba u flex ibier :Vli:-.chbest ands mode llc. Pora-v. C ~ 1. l 1.1-, 175- 1S7.
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Forest Ecology and Management
Forest Ecology and Management 120 (1999 ) 59-76
Simulation of tree and stand development under different environmental conditions with a physiologically based model R. Grote":", M , Erhard b "Institute f or Forest Gm .....th Research. University of Munich. Am Hochan ger 13. D· 85354 Freisin g. Germany t>Porsdam Institut e fo r Climate Impact Research. P.O. Box 60 1'2 03. D-/4412 Potsdam . Germany
Received 15 October 1997: accepted 28 October 1998
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