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

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68 Chapter 3 Age-related mortality The age-related probability of mortality is calculated by assuming that the annual tree mortality rate (gP m1,s ) is constant throughout tree life, which corresponds to the negative exponential curve for survivorship (Harcombe 1987, Eq. 3.29): gS t,s = e – gP m1,s ⋅ t (3.29) where gS t,s is the percentage of survivors of species s at time t. The value of gP m1,s can be determined by assuming that only a small fraction kP of the population reaches the age kAm s (Eq. 3.30): gP m1,s = –Ln(gS t,s) t = –Ln(kP) kAm s = kDeathP kAm s (3.30) Assuming kP = 0.01 yields kDeathP = 4.605, which is the default value of this parameter seen throughout the literature (Botkin et al. 1972a,b, Shugart 1984). Tab. 3.4: Symbols used in the mortality submodel of FORCLIM-P. Bold face denotes state variables. Factor Symbol Unit Explanation Eq. Age-dependent mortality gP m1,s %/100 mortality probability 3.30 kDeathP – mortality probability coefficient kAm s yr maximum tree age gS t %/100 fraction of population surviving up to time t 1) kP %/100 fraction of population that reaches kAm 1) s Stress-induced mortality gP m2,c %/100 mortality probability 3.31 SGr c – number of years a cohort has grown slowly 3.32 ƒ(e) c – effect of environment on max. growth rate 3.28 kMinAbsInc cm·yr -1 minimum absolute growth requirement kMinRelInc – minimum relative growth requirement kSGrYrs yr number of years a tree can grow slowly without being subject to stress-induced mortality kSlowGrP %/100 mortality rate of slow-growing trees Extrinsic disturbances gP m3 %/100 mortality probability 3.33 kDistP %/100 probability of occurrence of a disturbance Total mortality probability gP m %/100 probability that a tree dies in a given year 3.34 1) used for the derivation of the age-dependent mortality; not used in the simulation model.
The forest model FORCLIM 69 Stress-induced mortality Analogous to the age-related mortality, the increased mortality rate induced by environmental stress (gP m2,c ) is based on the assumption that only a small fraction of trees will survive a given number of years when they are subject to such stress (Shugart 1984, Pastor & Post 1985, Kienast 1987, Solomon & Bartlein 1993): gP m2,c = kSlowGrP SGr c > kSGrYrs 0 else (3.31) where SGr c is the the number of consecutive years the cohort's diameter has increased less than 10% of the maximum diameter increment (kMinRelInc) or less than 0.3 mm (kMinAbsInc). Hence, SGr c provides a memory for past environmental stress; therefore it is a state variable (Eq. 3.32): SGr c (t+1) = SGr c (t) + 1 ƒ(e) c < kMinRelInc ∨ ∆D c ∆t 0 else < kMinAbsInc (3.32) where t denotes the discrete time in years. Disturbance-related mortality As noted in section 3.1, the disturbance-related mortality is formulated in a simple manner, i.e. the probability that the trees on the patch are killed by a disturbance is regulated by the model parameter kDistP (Eq. 3.33): gP m3 = kDistP (3.33) Overall mortality probability Eq. 3.34 describes the calculation of the overall mortality probability for each tree and each year (gP m ). The trees are subject to the disturbance-related mortality first (gP m3 ); if they survive, they may die from the age-related mortality (gP m1,s ) and, finally, from the stress-induced mortality rate (gP m2,c ). In the simulation model, the overall mortality probability (gP m ) is determined for each tree using Monte Carlo techniques. gP m = gP m3 + (1 – gP m3 )·(gP m1,s + [1 – gP m1,s ]·gP m2,c ) (3.34)
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Diss. ETH No. 10638 On the Ecology
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ii Table of contents A BSTRACT.....
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iv APPENDIX .......................
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vi Harald BUGMANN, 1994: On the eco
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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 and 56: The forest model FORCLIM 61 Overall
Page 57 and 58: The forest model FORCLIM 63 D (cm)
Page 59 and 60: The forest model FORCLIM 65 a) b) c
Page 61: The forest model FORCLIM 67 Growth
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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