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

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78 Chapter 3 COV m,l = 2 σ T,m,l r PT,m,l · σ T,m,l · σ P,m,l r TP,m,l · σ T,m,l · σ P,m,l 2 σ P,m,l (3.65) The loadings of the principal component factors of the covariance matrix are calculated next (i.e. its denormalized Eigenvectors E 1 and E 2 , Eq. 3.66; Flury & Riedwyl 1983). Like this it is possible to obtain cross-correlated variates of temperature and precipitation according to Eq. 3.67 & 3.68: E 1 = eig(COV) 1 = E 11 E 12 , E 2 = eig(COV) 2 = E 21 E 22 (3.66) T m,y,l = µ T,m,l + cl T,m,y,l (3.67) P m,y,l = µ P,m,l + cl P,m,y,l (3.68) where X m,y,l is the actual mean monthly value of the variable (X ∈ {T,P}), and cl X,m,y,l is a linear combination of two independent normal variates v (v ~ N (0,1) ) multiplied by the components of the Eigenvectors (Eq. 3.69 & 3.70): cl T,m,y,l = v 1 · E 11 + v 2 · E 21 (3.69) cl P,m,y,l = v 1 · E 12 + v 2 · E 22 (3.70) CALCULATION OF BIOCLIMATIC VARIABLES Winter minimum temperature The approach presented by Fischlin et al. (1994) is used in FORCLIM-E (Eq. 3.71). uWiT ≡ Tw y,l = MIN( T Dec,y-1,l , T Jan,y,l , T Feb,y,l ) (3.71) Annual sum of degree-days In our analysis of climate-dependent factors in forest gap models (Fischlin et al. 1994) we compared the conventional method for calculating the annual degree-day sum (Botkin et al 1972a,b) with the more precise sine-wave method by Allen (1976), and we conjectured that the difference between the two methods increases the closer the mean monthly tem-
The forest model FORCLIM 79 perature is to the threshold temperature used for the summation. In the subsequent analysis, this hypothesis was tested, and a correction formula for obtaining more accurate estimates of the annual degree-day sum was developed. The estimates of monthly degree-days as produced by the approximation developed by Botkin et al. (1972a,b) and the more precise sine-wave method by Allen (1976) were compared at the sites Bern, Bever, Locarno, Davos, Basel, and Sion (cf. Appendix III). The former three sites were used to develop a model for the degree-day correction, and the latter three were used to validate it. The error in the estimation of the monthly sum of degree-days showed a remarkably similar pattern across all six sites (cf. Fig. 3.8 with the site Bern as an example). The hypothesis that the largest error can be found in the vicinity of the development threshold of 5.5 °C seems to be the main cause for the site-specific bias. Thus for FORCLIM-E an empirical correction formula was developed based on these data. To reveal the pattern underlying the data more clearly, the differences between Allen's and Botkin's estimation methods (Fig. 3.8) were averaged in temperature windows having a width of 1 °C, centered around every 0.5 °C (Fig. 3.9). Three separate regressions were fitted to these data, yielding an error function of the monthly degree-day estimation according to the conventional method (Fig. 3.9). 80 60 D (°C*d) 40 20 0 -20 -10 0 T 10 m,y,l (°C) 20 30 Fig. 3.8: Difference (D) between the estimation method for the monthly degree-day sum used in conventional forest gap models (Botkin et al. 1972a,b) and the more precise sinewave method by Allen (1976) as a function of the monthly mean temperature (T m,y,l ). Data from the site Bern (Appendix III).
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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
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1 1 . Introduction 1.1 Climatic cha
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Introduction 3 1.2 Methods for the
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Introduction 5 in a changing climat
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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 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: The forest model FORCLIM 77 NITROGE
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
Page 115 and 116: Parameter sensitivity & model valid
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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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