Climate Sensitive Tree Growth Functions and the Role of Transformations
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Forest Research Data
2.2. Explanatory Variables
2.2.1. Competition
2.2.2. Stand Development
2.2.3. Site
2.2.4. Stand Density
2.2.5. Thinning
2.2.6. Mixture
2.2.7. Climate
2.2.8. Years Past 1940
2.3. Model Fitting
2.3.1. Base Model
2.3.2. Transformation
- = sign(y) , with
- , with
2.3.3. Model Selection
2.3.4. Model Validation
3. Results
3.1. Role of Transformation
3.2. Climate Sensitive Growth Functions
3.2.1. Overview
3.2.2. Effects
Competition
Stand Development
Site
Stand Density
Thinning
Mixture
Climate
Non Significant Effects
4. Discussion
4.1. Transformation
4.2. Estimation Method
4.3. Estimated Effects
4.3.1. Explained Variance
4.3.2. Model Selection
4.3.3. Nitrogen
4.3.4. Years Past 1940
5. Conclusions
Supplementary Materials
Acknowledgments
Conflicts of Interest
Abbreviations
d | (single tree-specfic) tree diameter (at 1.3 m height, breast height) in cm |
dominant diameter in cm: quadratic mean of the 100 thickest trees per hectare | |
A | total plot area in hectares (104 m2) |
a | stand age in years |
tree basal area (at breast height) in m2: | |
total plot basal area in m2/ha: | |
ith year of the measurement | |
basal area increment normalized to 5-year period: | |
relative basal area increment: | |
cumulative basal area: | |
basal area of larger trees: | |
relative basal area of larger trees: | |
percentage of basal area previously harvested in relation to | |
total number of trees per hectare in a plot | |
percentage of stems harvested since last inventory | |
crown surface area in m2: with the imputed crown radius, the imputed crown length | |
crown base (height where the living crown starts), in m | |
crown cross sectional area in m2 | |
stand density index: | |
crown competition index Equation (2) | |
change in crown competition index after harvesting has taken place Equation (2) | |
leading tree species is coniferous (holding maximum basal area in a stand) | |
if the observation year is before 1940, it is zero, otherwise the current year of observation−1940. | |
p | yearly mean precipitation sum over period length in mm. Calculated for physiological year, meaning that the sum was taken from October until September, in contrast to calender years [42]. |
t | mean physiological year temperature, over intervals such as p. |
m | Aridity index (defined by deMartonne ([38], [p. 520])). . Since this index means smaller values have higher aridity, its inverse interpretation is more intuitive. Consequently it was labeled “moisture-index” (m). In contrast to precipitation and temperature, moisture shows higher explanatory power in the spring months [42]; hence only the spring months (March–June) over periods were used to calculate the moisture index. |
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Variable Units | bai m2/(5 years) | d cm | bal m2 | rbal - | cba - | cc - | a years | ddom cm | csa m2 | ndep kg/ha/year | slope % | Nor. - | Eas. - | sdi - | bat m2 | nt 1/ha | bah % | nh % | ccc - | mixB - | t °C | p mm | m mm/°C | Y.P. 1940 years | year - |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
min | −29.8 | 0.6 | 0.0 | 0.0 | 0.0 | 0.0 | 22 | 11.4 | 3.1 | 5.2 | 2.5 | −1.0 | −1.0 | 57 | 3.5 | 24 | 0.0 | 0.0 | 0.0 | 0.0 | 0.2 | 145 | 10.8 | 0 | 1904 |
5% | 0.2 | 6.2 | 4.3 | 0.1 | 0.0 | 0.5 | 34 | 16.4 | 23.6 | 11.1 | 2.5 | −1.0 | −1.0 | 489 | 17.9 | 342 | 0.0 | 0.0 | 0.0 | 0.0 | 3.4 | 747 | 14.4 | 0 | 1913 |
50% | 32.4 | 17.6 | 24.6 | 0.8 | 0.2 | 1.1 | 63 | 33.3 | 73.2 | 19.9 | 10.0 | 0.0 | 0.0 | 767 | 35.2 | 1050 | 0.1 | 0.1 | 0.1 | 0.1 | 7.9 | 1005 | 22.3 | 0 | 1936 |
95% | 181.0 | 46.4 | 46.9 | 1.0 | 0.6 | 2.4 | 154 | 58.2 | 294.0 | 37.1 | 50.0 | 1.0 | 0.7 | 1181 | 58.5 | 4060 | 0.2 | 0.3 | 0.3 | 1.0 | 9.1 | 1412 | 39.6 | 53 | 1993 |
max | 901.9 | 156.5 | 93.2 | 1.0 | 1.0 | 4.1 | 293 | 81.7 | 1206.9 | 60.6 | 80.0 | 1.0 | 1.0 | 1660 | 94.2 | 11,139 | 0.6 | 0.7 | 1.7 | 1.0 | 11.5 | 1693 | 54.0 | 72 | 2012 |
Group | Co. | Variable | Maple | Beech | Douglas Fir | Spruce | Pine | Larch | Oak | Fir |
---|---|---|---|---|---|---|---|---|---|---|
Diameter | Intercept | 5.858 | 1.150 | 2.680 | 5.429 | −6.390 | 7.339 | −7.538 | −1.750 | |
d | 16.13 | 20.30 | 36.18 | 19.08 | 19.89 | 21.12 | 21.66 | 19.48 | ||
d.exp | −0.01931 | −0.03512 | −0.02289 | −0.03172 | −0.02540 | −0.02407 | −0.03159 | −0.02711 | ||
bal | −0.060920 | −0.065076 | −0.075616 | |||||||
Competition | rbal | −4.482 | −2.030 | |||||||
cba | 1.404 | 0.845 | 3.520 | |||||||
Stand development | a | −0.05312 | −0.05535 | −0.34983 | −0.05592 | −0.08499 | −0.07945 | −0.06539 | ||
a2 | 0.0002020 | 0.0002173 | 0.0015429 | 0.0001668 | 0.0002086 | 0.0001778 | 0.0001548 | |||
ddom | 0.07733 | |||||||||
ndep | 0.073038 | −0.127648 | −0.010480 | −0.188290 | −0.111304 | 0.011745 | −0.168438 | −0.158790 | ||
ndep2 | 0.002485 | 0.002982 | 0.001768 | 0.000970 | 0.003283 | 0.002066 | ||||
slope | −0.2442 | 0.0029 | ||||||||
northness | −0.2485 | |||||||||
Site | eastness | 1.3340 | 0.1786 | 0.4530 | ||||||
relief.depres. | −0.9685 | |||||||||
relief.slope | −0.6542 | −0.4546 | 0.2175 | |||||||
relief.summit | −0.1927 | −0.8402 | 0.9349 | |||||||
relief.slope.toe | 0.6588 | −1.7911 | ||||||||
Stand density | sdi | −0.002934 | −0.003622 | |||||||
bat | −0.20652 | −0.07191 | −0.06243 | −0.05675 | 0.02064 | −0.02525 | ||||
bat2 | 0.001587 | 0.000363 | −0.001909 | −0.000830 | ||||||
bat(nt) | 0.00349 | 0.01100 | ||||||||
(nt) | 0.6270 | 2.2025 | ||||||||
Thinning | treat | 0.5474 | 0.1521 | 1.7647 | 0.5355 | −0.2515 | ||||
bah | 0.0208 | 1.9846 | ||||||||
ccc | −2.209500 | |||||||||
Mixture | mixB | −2.893 | −2.830 | −2.419 | −1.911 | |||||
lead.con | 1.405297 | 1.189001 | ||||||||
Climate | t | −0.3261 | 0.3434 | 1.9871 | 0.0866 | 2.4940 | −0.2539 | 3.0467 | −1.1924 | |
p | 0.00170 | 0.00089 | 0.00070 | −0.00111 | −0.00272 | −0.00619 | 0.00116 | −0.00188 | ||
m | 0.3422 | 0.1934 | −0.3176 | 0.1019 | 0.6144 | −0.2154 | −0.4253 | −0.1410 | ||
−0.0000504 | −0.0001068 | −0.0011325 | 0.0008349 | −0.0000792 | ||||||
0.0545 | −0.0401 | 0.0363 | 0.0300 | |||||||
t2 | −0.1672 | −0.0078 | −0.1312 | −0.0397 | −0.1637 | 0.0656 | ||||
p2 | 0.00000205 | 0.00001383 | 0.00000274 | −0.00000949 | 0.00000163 | |||||
m2 | −0.00761932 | −0.00196531 | 0.00007983 | 0.01552329 | 0.00251696 | −0.00806958 | 0.00146262 | |||
Unexplained | year.past1940 | 0.0298 | 0.0227 | 0.0924 | 0.0320 | 0.0295 | 0.0401 | 0.0196 |
Tree species | Maple | Beech | Douglas | Spruce | Pine | Larch | Oak | Fir |
---|---|---|---|---|---|---|---|---|
n | 2450 | 149,009 | 9759 | 190,047 | 13,452 | 24,807 | 44,799 | 139,977 |
(%) | 68.66 | 73.91 | 72.08 | 62.13 | 47.18 | 56.97 | 80.36 | 67.73 |
(%) | 56.94 | 72.18 | 68.15 | 60.04 | 38.83 | 40.65 | 78.87 | 66.30 |
(cm2/(5 years)) | 21.70 | 22.67 | 60.53 | 31.56 | 33.86 | 45.20 | 26.19 | 54.89 |
(cm2/(5 years)) | 25.44 | 23.41 | 64.65 | 32.42 | 36.43 | 53.09 | 27.17 | 56.10 |
(%) | 73.31 | 63.93 | 53.44 | 61.97 | 53.03 | 58.70 | 52.33 | 78.04 |
(%) | 85.94 | 66.01 | 57.07 | 63.65 | 57.06 | 68.94 | 54.28 | 79.76 |
robust residual | 1.52 | 1.38 | 2.34 | 1.80 | 1.91 | 2.22 | 1.46 | 2.08 |
weights, smaller 1 (in %) | 22.57 | 20.93 | 20.48 | 20.29 | 19.54 | 20.31 | 19.59 | 20.36 |
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Zell, J. Climate Sensitive Tree Growth Functions and the Role of Transformations. Forests 2018, 9, 382. https://doi.org/10.3390/f9070382
Zell J. Climate Sensitive Tree Growth Functions and the Role of Transformations. Forests. 2018; 9(7):382. https://doi.org/10.3390/f9070382
Chicago/Turabian StyleZell, Jürgen. 2018. "Climate Sensitive Tree Growth Functions and the Role of Transformations" Forests 9, no. 7: 382. https://doi.org/10.3390/f9070382