On the Ecology of Mountainous Forests in a Changing Climate: A ...

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62 Chapter 3 In most forest gap models Eq. 3.9 is used to predict optimum diameter growth (Shugart 1984, Botkin 1993). However, the formulation of Eq. 3.8 conceals the assumptions about the “cost associated with tree size”, i.e. respiration. It can be hypothesized that maintenance respiration should be proportional e.g. to stem volume or stem surface (Kinerson 1975); reconstructing from Eq. 3.8 an equation where the formulation of respiration is explicit (see Moore 1989), we obtain ∆V c ∆t = kR · gL c – kS · V c · D c (3.10) Thus, in the conventional growth equation maintenance respiration is assumed to be proportional to a power higher than tree volume, which is not realistic. In view of this limitation, Moore (1989) developed an equation for tree diameter increment from a simple carbon budget of the tree: Considering biomass (volume) increment and assuming that (a) gross photosynthesis is proportional to leaf area gL c and (b) respiration is proportional to stem volume V c , we can write ∆V c ∆t = kR · gL c – kS · V c (3.11) Next we assume the following allometric relationships: (c) gL c = k 1·D c 2 (Whittaker & Marks 1975) (3.12) (d) gH c = 137 + kB 2,s·D c + kB 3,s·D c 2 (Ker & Smith 1955) (3.13) (e) V c = k 2·D c2·gH c (the volume of a cone) (3.14) Using these assumptions, the following equation for diameter increment is obtained (for the details of the derivation, see Moore 1989): ∆D c ∆t = kG s ⋅ D c ⋅ 1 - gH c kHm s 2 274 + 3⋅kB 2,s ⋅D c + 4⋅kB 3,s ⋅D c · ƒ(e) c (3.15) where ƒ(e) c is a multiplier used to reduce maximum growth according to the environmental constraints described below. This equation has a form similar to the conventional equation (Eq. 3.9), but its assumptions conform more to biological expectations. Thus it is used to predict the diameter increment in FORCLIM-P (Fig. 3.6).
The forest model FORCLIM 63 D (cm) 300 Fagus silvatica gH (m) 60 D (cm) 300 Larix decidua gH (m) 60 200 gH 40 200 gH 40 100 D 20 100 D 20 0 0 100 200 Time (years) 0 300 0 0 100 200 Time (years) 0 300 Fig. 3.6: The maximum growth equation (Eq. 3.15) simulated for beech (Fagus silvatica, left) with kG s = 191 cm/year, kHm s = 45 m, and kDm s = 225 cm, and larch (Larix decidua, right) with kG s = 170 cm/year, kHm s = 52 m, and kDm s = 185 cm. D c (0) is 1.27 cm, and the discrete time step (∆t) is one year. Finally, from the evaluation of Eq. 3.13 when ∂gH c /∂D c = 0 at gH c = kHm s and D c = kDm s , the parameters kB 2,s and kB 3,s can be expressed as functions of maximum height and maximum diameter alone: kB 2,s = 2 · (kHm s – 137) kDm s (3.16) kB 3,s = – kB 2,s 2 · kDm s (3.17) Light growth factor The calculation of the light growth factor follows the descriptions by Botkin et al. (1972a,b) and Shugart (1984): Beer's extinction law is used to calculate the available light at the height of cohort c as a function of leaf area index: gAL gHc = e - kLAtt ⋅ gCumLA gHc (3.18) where gCumLA gHc is the cumulative leaf area index at the height of cohort c (Eq. 3.19), summed over all cohorts based on the relationships given in Eq. 3.20 & 3.21 for calculating the double-sided foliage area (gFolA c ) from foliage dry weight (gFolW c ) (Burger 1945-1953):
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Diss. ETH No. 10638 On the Ecology
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ii Table of contents A BSTRACT.....
Page 6 and 7: iv APPENDIX .......................
Page 8 and 9: vi Harald BUGMANN, 1994: On the eco
Page 10 and 11: viii Harald BUGMANN, 1994: Aspekte
Page 13 and 14: 1 1 . Introduction 1.1 Climatic cha
Page 15 and 16: Introduction 3 1.2 Methods for the
Page 17 and 18: Introduction 5 in a changing climat
Page 19 and 20: Introduction 7 Their integrative ca
Page 21 and 22: Introduction 9 (1984) provides a mo
Page 23 and 24: Introduction 11 The main advantage
Page 25 and 26: 13 2 . Analysis of existing forest
Page 27 and 28: Analysis of existing forest gap mod
Page 39 and 40: The forest model FORCLIM 45 carbon
Page 41 and 42: The forest model FORCLIM 47 TREE GR
Page 43 and 44: The forest model FORCLIM 49 gBFlag
Page 45 and 46: The forest model FORCLIM 51 Disturb
Page 47 and 48: The forest model FORCLIM 53 decay o
Page 49 and 50: The forest model FORCLIM 55 the est
Page 51 and 52: The forest model FORCLIM 57 3.3 Mod
Page 53 and 54: The forest model FORCLIM 59 Light a
Page 55: The forest model FORCLIM 61 Overall
Page 59 and 60: The forest model FORCLIM 65 a) b) c
Page 61 and 62: The forest model FORCLIM 67 Growth
Page 63 and 64: The forest model FORCLIM 69 Stress-
Page 65 and 66: The forest model FORCLIM 71 Tab. 3.
Page 67 and 68: The forest model FORCLIM 73 3.3.2 F
Page 69 and 70: The forest model FORCLIM 75 where k
Page 71 and 72: The forest model FORCLIM 77 NITROGE
Page 73 and 74: The forest model FORCLIM 79 peratur
Page 75 and 76: The forest model FORCLIM 81 of degr
Page 77 and 78: The forest model FORCLIM 83 microcl
Page 79 and 80: The forest model FORCLIM 85 Tab. 3.
Page 81 and 82: The forest model FORCLIM 87 3.4.3 F
Page 83 and 84: The forest model FORCLIM 89 All the
Page 85 and 86: The forest model FORCLIM 91 The mas
Page 87 and 88: The forest model FORCLIM 93 FORCLIM
Page 89 and 90: Behaviour of FORCLIM along a transe
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Behaviour of FORCLIM along a transe
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Parameter sensitivity & model valid
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153 6 . Model applications Climatic
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Model applications 155 The simulate
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Model applications 157 6.2 Possible
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Model applications 159 simulation s
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Model applications 161 Simulation e
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Model applications 163 At the site
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Model applications 165 Bever Biomas
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Model applications 167 tainty inher
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Model applications 169 scenario cho
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Discussion 171 Finally, the analysi
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Discussion 173 bitrarily chosen par
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Discussion 175 comparably small imp
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Discussion 177 end of the 21st cent
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Conclusions 179 Ecological factors
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Conclusions 181 species composition
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References 183 Begon, M., Harper, J
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References 185 Burger, H., 1951. Ho
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References 187 Faber, P.J., 1991. A
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References 189 Huntley, B. & Birks,
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References 191 Leemans, R. & Prenti
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References 193 Olson, J.S., 1963. E
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References 195 Rudloff, W., 1981. W
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References 197 Smith, T.M., Leemans
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References 199 Whittaker, R.H., 195
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Appendix 201 II. Derivation of para
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Appendix 203 Tab. A-4: Tree species
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Appendix 205 Tab. A-7: Values for m
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Appendix 207 The minimum winter tem
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Appendix 209 Tab. A-11: Shade toler
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Appendix 211 Tab. A-14: Climatic pa
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Appendix 213 IV. Source code of the
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Appendix 215 FROM SimBase IMPORT De
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Appendix 217 END; (* IF *) prevDay
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Appendix 219 PROCEDURE InitializeFW
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Appendix 221 InstallSeparator( fMen
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Appendix 223 FROM FCPFileIO IMPORT
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Appendix 225 modelSp^.p.kHm := sens
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Appendix 227 DeclMV( meanLitt[leafS
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Appendix 229 Swiss Federal Institut
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Appendix 231 (*********************
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Appendix 233 BEGIN WITH sp^ DO d :=
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Appendix 235 Definition module FCPB
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Appendix 237 Purpose Simulation mod
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Appendix 239 END Immobilization; PR
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Appendix 241 CONST lem = 3; VAR ef:
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Appendix 243 Purpose Provides the b
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Appendix 245 Example of a text file
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Appendix 247 Tab. A-15: Lower end o
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Appendix 249 Tab. A-17: Percentage
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Appendix 251 Tab. A-19: Significant
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Appendix 253 VI. Derivation of para
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Appendix 255 Tab. A-21: Species-spe
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Appendix 257 Tab. A-22 (continued)
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