Forestry
An International Journal of Forest Research
Forestry 2016; 89, 364–372, doi:10.1093/forestry/cpw014
Advance Access publication 27 February 2016
Climate and height growth of taiwania (Taiwania cryptomerioides) and
Taiwan incense-cedar (Calocedrus formosana) in Taiwan
C.-M. Chiu1, C.-T. Chien1, G. D. Nigh2* and C.-H. Chung1
1
2
Taiwan Forestry Research Institute, 53 Nan-Hai Road, Taipei 10066, Taiwan, ROC
Ministry of Forests, Lands and Natural Resource Operations, PO Box 9512, Stn. Prov. Govt., Victoria, BC V8W 9C2, Canada
*Corresponding author. Tel: +1 2503873093; Fax: +1 2509533838; E-mail: [email protected].
Received 21 September 2015
Taiwan incense-cedar (Calocedrus formosana (Florin) Florin) and taiwania (Taiwania cryptomerioides Hayata) are
coniferous species growing in Taiwan, Republic of China. Both species are red listed, and hence, their management
and conservation are important. The objective of this research was to determine the effect of climate on the height
growth of Taiwan incense-cedar and taiwania. Height growth data for Taiwan incense-cedar came from stem analysis data and the data for taiwania were from three sets of experimental plots. Climate data were obtained from
nearby climate stations. Dynamic height growth models having parameters that were functions of climate variables were fit to the height data. A Chapman–Richards function formed the basis for Taiwan incense-cedar
model, and a linear model was fit to the taiwania data. Mean summer temperature and precipitation were predictor variables for Taiwan incense-cedar height growth. These variables, along with growing degree-days, were predictor variables for taiwania. Several scenarios were devised to show the effect of climate on height growth. Under
the A1B climate change scenario, the height growth of taiwania is expected to increase, but the height growth of
Taiwan incense-cedar will decrease slightly. The climate/height growth relationships can assist in the conservation
and stewardship of these species.
Keywords: climate change, dynamic model, growing degree-days, mean summer precipitation, mean summer temperature, red listed
Introduction
Taiwan, Republic of China, is a nation lying on the Tropic of Cancer in
the Pacific Ocean, east of China. About half of Taiwan is mountainous
with .200 peaks above 3000 m in elevation. The vegetation of
Taiwan reflects both Taiwan’s geographic location and mountainous
terrain. Vegetation zones range from subalpine to tropical with temperature and precipitation being the main determining factors (Li
et al., 2013). The northern and central regions of Taiwan are subtropical, the south is tropical and the mountainous regions are temperate. The following is a brief description of Taiwan’s climate since it
is integral to this research. The temperature in Taiwan ranges from
moderate to hot and is mostly dependent on elevation (Li et al.,
2013). Freezing temperatures and snow can occur at higher elevations. The winter and summer East Asian monsoon systems strongly
influence precipitation (Central Weather Bureau, 2015). The winter
monsoons (October–March) bring moderate precipitation to the
northern and eastern regions of Taiwan, whereas the central and
southern regions are sunny and receive little rainfall in the winter.
The summer monsoons are in May and June and rainfall can be
heavy. Typhoons are most frequent from July to September and
can bring torrential and sustained damaging rainfall.
The focus of this study is on the coniferous species Taiwan
incense-cedar (Calocedrus formosana (Florin) Florin) and taiwania
(Taiwania cryptomerioides Hayata). Taiwan incense-cedar is found
at lower elevations than taiwania, but their elevation ranges
overlap and they can be found together in mixed species stands.
Both of these species are considered by the International Union
for Conservation of Nature and Natural Resources (IUCN) to be
threatened, meaning that they have a higher risk of extinction.
The IUCN classifies taiwania as being vulnerable (Thomas and
Farjon, 2011) and Taiwan incense-cedar is endangered (Yang
et al., 2013).
The climate in Taiwan is changing (Hsu et al., 2011). Temperatures
in Taiwan over the last 100 years have been increasing at a rate of
0.148C per decade. However, therate of increase in temperature is accelerating; the warming rate in the last 30 years has been 0.298C per
decade. Temperature increases are not constant across Taiwan. They
have been most prominent in autumn, but in the last 30 years, the
temperature increases have been greatest in the winter. Precipitation
over the same period has been relatively constant although the
number of days with rain has been decreasing. The projected
climate in the future depends on the scenario and model that are
used to make projections. Projections made by the Taiwan Climate
Change and Information Platform project (Lin et al., 2013) using
the Intergovernmental Panel on Climate Change scenario A1B (Intergovernmental Panel on Climate Change, 2000), which is considered
to be the most likely scenario, indicate that by the year 2100, the
# Crown copyright 2016.
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Climate/height growth relationships for Taiwania and Calocedrus
temperatures will have increased by 2–38C compared with 100 years
ago. Over the same time period, summer precipitation is expected to
increase, but winter precipitation is projected to decrease. These
changes may cause the coniferous forests at mid- to high elevations
to move upwards, which will further reduce the range of some
species (Council for Economic Planning and Development, 2012).
The objective of this research is to determine the effects of
climate on height growth of two threatened species mostly
found in Taiwan: taiwania and Taiwan incense-cedar. While it is
well known that temperature and precipitation affect tree growth
(e.g. Kozlowski and Keller, 1966; Landsberg, 1986), this research
will result in a better understanding of the effects of climate
change on tree growth of these species. A modelling approach
was taken to address this question. The goal was to show how
climate affects height growth by expressing the parameters of a
height growth model as functions of climate variables.
Materials and methods
The data for this project are from experiments that were designed for purposes other than to examine the relationships between climate and
growth. Tree selection criteria from site index research, which involves
selecting sample trees whose growth has not been affected by non-site
factors (e.g. Hann and Scrivani, 1987; Mailly et al., 2004), were used to
avoid confounding growth due to climate with growth due to non-climatic
factors such as suppression and, in particular, silvicultural interventions.
The main criterion for selecting sample trees from the study plots is to
select the tallest trees from plantations and using height as the response
variable since it is minimally affected by thinning and pruning (Pokharel
and Froese, 2009; Mäkinen et al., 2014).
Taiwan incense-cedar data
The data for Taiwan incense-cedar come from three plantations established in 1928, 1954 and 1959 in the Lianhuachih Research Center forest
in central Taiwan (more details about the sample trees can be found in
Chiu et al. 2015). The oldest plantation was thinned in 1948, 1954 and
1975, and the plantation established in 1954 was thinned in 1974. The
youngest plantation was not thinned, but it was pruned in 1971. The
trees were destructively sampled in 2004, 2006 and 2008 by sectioning
at 0.3 m, 1.3 m and then at 2.0 m intervals. Occasionally an additional
section was taken near the top of the tree. All trees were sectioned using
the same protocols. Only data from the three (2006 and 2008 samples)
or four (2004 sample) largest trees were used in the analysis. The diameter
at breast height (DBH) and total height of the trees were also recorded. The
heights of the tips of the tree immediately above the sectioning points were
determined with the procedure described by Newberry (1991) and their
ages were determined from the ring counts.
The climate data came from a weather station (longitude 1208 54′ E,
latitude 238 56′ N, elevation 744 m) located 1 –2 km from the study
sites and at approximately the same elevation. Daily minimum, mean
and maximum temperatures, as well as daily precipitation, were recorded.
Climate data from 1961 until 2013 were available.
height caused some of the trees to have large increases in height at the
transition measurement, and any change in predicted height is actually a
diameter response, not a height response. Therefore, only data for the measurements where height was recorded were analysed. The equivalents of
the 100 tallest trees per hectare (i.e. the number of trees was scaled by
the plot size) from each plot were used as the sample trees, resulting in
choosing four or six trees per plot. The tallest trees were selected based
on the tree height at the last measurement where height was measured.
Preliminary investigations showed that the height growth data from plots
within an installation were spatially correlated. Therefore, only three plots
within an installation were analysed to reduce this correlation. The criteria
for choosing the three plots were that they had the lowest height, highest
height and the height closest to the midpoint between the lowest and
highest heights, based on the last measurement. These plots provided
the greatest range of information for each installation.
A local weather station (longitude 1208 42′ E, latitude 238 00′ N, elevation 1510 m) provided the climate data from 1980 to 2013, excluding data
for 1996– 1998 that were missing and could not be recovered. This station
was located ,1 km from the Lioukuei compartment 3 site. The Lioukuei
compartment 12 site was 2– 3 km from the weather station and at the
same elevation. The Tengzhih site was 5 km from the station and at an
elevation of 1300 m. As with the Lianhuachih weather station, daily
minimum, maximum and average temperatures and precipitation were
available.
Climate data summary
The climate data from both sites were summarized in the same manner.
The minimum, maximum and average daily temperatures were averaged
by month, and daily precipitation was summed by month. Both climate stations had missing records that could not be recovered. If there were 20 or
more days of data, the temperature averages were retained as calculated,
but the precipitation data were pro-rated based on the available data for the
month and the number of days of missing data. If there were ,20 days of
data for a climate variable in a month, then the climate variable for that
month was predicted as the average for the same month from the previous
3 years and the following 3 years of data. This method of handling missing
data will capture trends in climate, if any. The averaging was done with procedure EXPAND in SAS (SAS Institute Inc., 2011).
The following climate variables were calculated from the monthly
climate data:
Taiwania data
† Mean annual temperature (MAT, 8C): monthly average temperature averaged over the year.
† Mean annual precipitation (MAP, mm): sum of the monthly precipitation
for the year.
† Mean temperature of the coldest month (MTCM, 8C): average January
temperature.
† Mean temperature of the warmest month (MTWM, 8C): average temperature of the warmest month in a calendar year.
† Mean summer temperature (MST, 8C): monthly temperature averaged
over the summer months.
† Mean summer precipitation (MSP, 8C): sum of the monthly precipitation
for the summer months.
† Annual heat: moisture ratio (AHM, 8C mm21): MAT/MAP.
† Summer heat: moisture ratio (SHM, 8C mm21): MST/MSP.
† Growing degree-days above 58C (GDD, 8C days): 365×[(average daily
maximum temperature + average daily minimum temperature)/2–5].
The data for taiwania came from two thinning experiments located at
Tengzhih and Lioukuei. Both of these test sites are in Kaohsiung City, southcentral Taiwan. There were two compartments (sets of experimental plots)
at the Lioukuei site. Height was initially measured on all trees, but later
re-measurements used height– diameter models to predict height. This
created two issues: the transition from measured height to predicted
The coldest month in a year was usually December or January. However,
since the temperature in December of year ‘Y’ cannot affect the growth in
year ‘Y’, the coldest month for year ‘Y’ was assumed to be January. The
warmest month in a year was usually July. The summer months are
March–October, inclusive, based on the growing season beginning and
end dates determined from the work of Chang et al. (2011) and Chung
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and Kuo (2005). The formula for GDD was taken from Guan et al. (2009),
who used daily temperature to calculate GDD. The Guan et al.’s (2009)
GDD formula was modified since a complete daily record of temperature
does not exist. For sites that rarely go below 58C (as is the case with these
test sites), the two methods give virtually the same value for GDD. The
trends in the annual data for the climate variables in the final fitted
model were assessed with plots of the data and fitted trend lines.
The climate data were averaged over the years between consecutive
measurements for taiwania and between consecutive sectioning points for
Taiwan incense-cedar. That is, the climate data were averaged so that the
averages correspond to the same time periods as the growth measurements.
Annual height between measurements or sectioning points could have been
determined through linear interpolation and correlated with annual climate.
However, this was not done because the interpolation procedure averages
the variability in annual growth that may be due to variation in the annual
climate and hence could mask the effects of climate on growth. Instead,
height growth between the measurements/sectioning points and the
climate data for the corresponding time periods was analysed.
Analysis
The data were analysed by fitting a height projection model to the height and
age data and determining the effect that climate has on the model parameters. This approach is similar to the one taken by Meldahl et al. (1998).
A plot of the data (Figure 1) indicates that a Chapman– Richards model
(model 1) (Richards, 1959; Pienaar and Turnbull, 1973; Nishizono, 2010) and
a simple linear model (model 2) will describe the height trajectory for
Taiwan incense-cedar and taiwania, respectively.
hij = a0 × (1 − ea1 ×tij )a2 + 1ij
(1)
hij = a0 + a1 × tij + 1ij
(2)
where hij is the height (m) of tree/plot i at measurement j; tij the age (years) of
tree/plot i at measurement j; a0, a1 and a2 are model parameters to be estimated and 1ij is the random error term for tree/plot i at measurement j. The 1ij
are assumed to independently and identically normally distributed with
common variance s2.
The projection form of the height models (e.g. Nishizono 2010) was used
to make a dynamic system. A projection model takes a known point on the
response surface and projects the response forward, or less likely, backward
in time. The height projection models were derived by taking a known height
at a known age (i.e. hij ¼ hi0 at ti0) for tree/plot i and then expressing one parameter in the model as a function of hi0, ti0 and the other parameters. These
algebraic manipulations force the model to go through the known point.
Height projections are then made from this point. Three projection models
could be derived from model (1) for Taiwan incense-cedar; all three models
were investigated to find the best-fitting formulation. These models are
the same as model (1) except the following parameters are derived rather
than estimated:
a0 =
hi0
(1 − ea1 ×ti0 )a2
ln 1 − (hi0 /a0 )1/a2
a1 =
ti0
a2 =
ln(hi0 /a0 )
ln(1 − ea1 ×ti0 )
(3a)
(3b)
(3c)
Only one height projection model was derived from model (2) for taiwania.
Parameter a0 is expressed as:
a0 = hi0 − a1 × ti0
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Figure 1 Graphs of height vs age for Taiwan incense-cedar (a) and taiwania
(b). Solid lines show the measured growth trajectories and the dots are
predicted heights.
(4)
The next step in formulating the model is to allow the remaining parameters
to be linear functions of the climate variables. There are nine climate variables
available for analysis as described in the Climate data summary section. Many
of the climate variables are highly correlated with each other since they are
derived from the same data. For example, MAP is highly correlated with MSP
(r ¼ 0.98446 for the Lioukuei climate station data and r ¼ 0.95686 for the
Lianhuachih station). The correlation for these two particular variables
arises because most of the precipitation falls in the summer. Correlation
between predictor variables leads to multicollinearity, which inflates the variances of the parameter estimates, makes the effect of variables on the response variable difficult to interpret and can lead to counter-intuitive
results (Sen and Srivastava, 1990). These effects are detrimental to this
Climate/height growth relationships for Taiwania and Calocedrus
type of research because the focus is on scientific discovery as much as prediction. Therefore, multicollinearity was reduced by identifying a subset of
climate variables that were not highly correlated with each other and only
analysed those variables. Variables that were excluded from the analyses
were highly correlated with one or more variables in the inclusion subset
but were considered to be less biologically significant to tree growth than
the correlated variable in the inclusion subset. The variables that were in
the inclusion subset were MST, MSP, MTCM and GDD. Equation (5) shows
how parameter a1 in models (1) and (2) were expressed as linear functions
of the inclusion climate variables. Their interactions (products) were also
included in these functions.
a1 = a10 + a11 × MSTj + a12 × ln(MSPj ) + a13 × MTCMj + a14 × GDDj
+ a15 × MSTj × ln(MSPj ) + a16 × MSTj × MTCMj + a17 × MSTj × GDDj
+ a18 × ln(MSPj ) × MTCMj + a19 × ln(MSPj ) × GDDj + a110 × MTCMj × GDDj
(5)
where the climate variables are described as above, aik, k ¼ 0, 1, 2, 3, . . ., 10 are
parameters to be estimated, j indexes the measurement interval and ln is the
natural logarithm function. Similar equations were developed for parameters
a0 and a2 in model (1). The natural logarithms of MSP were taken since preliminary analyses showed that the logarithm of MSP resulted in better fitting
models.
The final step in formulating the models was to include random effects for
the intercept parameters a00, a10 and a20, whichever was applicable for a particular formulation. The random effects accounted for within tree/plot serial
correlation. Therefore, tree (for Taiwan incense-cedar) or plot within site (for
taiwania) was the subject and the random effects were assumed to be normally distributed with a mean of 0 and have a non-zero variance and covariance, which were estimated along with the fixed-effects parameters.
The projection formulation of models (1) and (2) with parameterizations
(3a), (3b), (3c) and (4) were fit using maximum likelihood in a mixed-effects
framework (Davidian and Giltinan, 1995) with procedure NLMIXED in SAS
(SAS Institute Inc., 2011). Model fit was evaluated with Akaike’s information
criterion (AIC) (Kutner et al., 2005). The following stepwise approach to
model fitting was taken due to difficulties in getting convergence to the solution for a model that included all parameters. A model without climate
variables but with the random effects was initially fit to the data. Climate
variables and their associated parameters were introduced into the
model one at a time. The climate variable that resulted in the lowest AIC
was kept in the model. The best two-variable model was then found in
the same way. This process was repeated until no other variables reduced
the AIC. The residuals from the final fitted model were then checked for normality with the Shapiro– Wilk statistic (Shapiro and Wilk, 1965), and trends
in the variance of the residuals were checked by plotting the residuals
against age, predicted height and the climate variables that were in the
model. Plots of actual and predicted growth trends were made to assess
the fit of the models. The fit of the models was also assessed by re-fitting
the same models without the climate variables to determine the effect of
the climate variables on the fit statistics.
Climate change scenarios were created to run in simulations with the
fitted models to assist in assessing the effects of various states of climate
change on height growth. Actual climate data for the scenarios were
used to avoid inadvertently obtaining an unlikely combination of climate
variables, for example a high MSTand a low GDD. The climate data selection
process began with normalizing the variables in the fitted models (MST, MSP
and GDD) from each climate station by subtracting their mean and dividing
by their standard deviation. Three statistics were calculated from the normalized data for taiwania: (MST + GDD)/2 + MSP, (MST + GDD)/2 2 MSP
and (|MST| + |GDD|)/2 + |MSP|), where | | is the absolute value operator.
For Taiwan incense-cedar, the following statistics were calculated with
the normalized climate variables: MST + MSP, MST 2 MSP and |MST| +
|MSP|. High values of the first statistic represent hot and wet climates,
Table 1 DBHs, heights and total ages of the 10 Taiwan incense-cedar
sample trees from the Lianhuachih forest
Tree ID
Sample
year
DBH (cm)
Height (m)
Total age
(years)
IC04_10
IC04_11
IC04_12
IC04_13
IC06_0_1
IC06_1_54_1
IC06_3_242_1
IC08_E
IC08_J
IC08_L
2004
2004
2004
2004
2006
2006
2006
2008
2008
2008
41.0
48.1
38.2
44.4
32.6
32.3
38.8
26.5
26.0
21.7
24.9
24.8
24.6
27.0
24.7
24.7
23.4
21.0
20.8
21.8
76
76
76
76
76
51
76
51
50
48
and low values represent cold and dry climates. The second statistic indicates cold and wet climates for low values and hot and dry climates for
high values. Low values of the third statistic represent average climates.
The climate variables giving the highest values for the first two statistics
and the lowest value for all three statistics were used in the simulations.
The National Science Council has projected that the temperature in
Taiwan will increase by 2– 38C and precipitation will increase by between
2 and 22 per cent in the rainy season over a 100-year time span (Council
for Economic Planning and Development, 2012). These projections are
based on the Intergovernmental Panel on Climate Change A1B scenario,
which is considered to be the most likely future outcome. Therefore, an
A1B run where the average temperature increases by 28C and average
precipitation increases by 20 per cent was included in the simulations.
For taiwania, the projected GDD is predicted from the linear relationship
between GDD and MST (GDD ¼ 2685.42 + 290.54×MST), which was
derived from the observed climate data.
A tree of approximately average height at age 10 (10 m for taiwainia; 7 m
for Taiwan incense-cedar) was assumed to get values for h0 and t0. The
random-effects parameters were set to 0. To examine the effects of
climate on the growth trajectories, the climate was changed annually and
linearly after age 10 so that after 100 years (200 years for MSP except for
the A1B scenario), the climate would be at the values chosen above. The
year-to-year variability for MSP was large, which led to large annual deviations from the mean for the wet and dry MSPs used in the simulations. Consequently, the time horizon for MSP in the wet and dry scenarios was set to
200 years to achieve reasonable changes in precipitation. Height was predicted for each year. The simulations were run to age 70 for Taiwan incensecedar and from age 10 to 25 for taiwania.
Results
The DBHs, heights and total ages of the Taiwan incense-cedar
sample trees are given in Table 1. Table 2 contains a summary of
the taiwania dataset.
The best-fitting model for Taiwan incense-cedar height based
on the AIC is model (1) with parameter a2 given by equation (3c)
and parameters a1 and a2 given by:
a0 = 1.1206 × MST + u
a1 = −0.6259 + 0.07816 ln(MSP)
where u is a random effect with a variance of 1.1131. The bestfitting model for taiwania height is model (2) with parameter a0
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Table 2 Summary data for the taiwania plots used in the analysis
Site
Number
of plots
Tengzhih
Lioukuei
Compartment 3
Compartment 12
3
3
3
Number of
observations
Plot size
(ha)
Number of
growth intervals
Age range
(years)
Height
range (cm)
6
0.06
2
17 –25
16.1– 22.7
11
18
0.04
0.04
4a
6
9 –20
11 –17
8.5– 17.0
10.3– 16.6
a
Exception: one plot had three growth intervals.
Table 3 Results of the data analysis for Taiwan incense-cedar and taiwania
Species
Parameter
Taiwan incense-cedar
Taiwania
Name
Estimate
SE
a01
a10
a12
s 2(u)a
a10
a11
a12
a14
a17
s 2(u)a
1.1206
20.6259
0.07816
1.1131
2214.88
8.3270
20.2076
0.03135
20.001202
0.01901
0.02776
0.2104
0.02759
0.6952
86.5614
3.2856
0.1125
0.01216
0.0004619
0.009545
Number of
observations
Error
variance
AIC
69
0.1754
106.9
35
0.01791
20.6
a
The variance of the random effect associated with a00 for Taiwan incense-cedar and a10 for taiwania.
given by equation (4) and parameter a1 given by:
a1 = −214.88 + u + 8.3270 × MST − 0.2076 ln(MSP) + 0.03135
× GDD − 0.001202 × MST × GDD
where u is a random effect with a variance of 0.01901. Standard
errors and fit statistics for these equations are presented in
Table 3. The variables MST, MSP and GDD were found to be the
best predictors of height growth and are plotted in Figure 2 for
the Lianhuachih (Taiwan incense-cedar) and Lioukuei (taiwania)
climate stations. The full range of available data is plotted, but
only the data from 1961 to 2007 (for Taiwan incense-cedar) and
from 1981 to 1996 (for taiwania) were used in the analysis.
Specifically, the final fitted models for Taiwan incense-cedar
and taiwania height are, respectively:
h = (1.1206 × MST + u) × (1 − e(−0.6259+0.07816 ln(MSP))×t )a2
where
a2 =
368
ln(h0 /(1.1206 × MST + u))
,
ln(1 − e(−0.6259+0.07816 ln(MSP))×t0 )
and
h = h0 + (−214.88 + u + 8.3270 × MST − 0.2076 ln(MSP)
+ 0.03135 × GDD − 0.001202 × MST × GDD) × (t − t0 )
In these models, h0 is a known height at known age t0, t is the age
for which height (h) is to be predicted, u is a random effect and the
climate variables are described previously.
The residuals from both models did not show any trends when
plotted against age, predicted height or climate predictor variables,
nor were they significantly different from 0 (a ¼ 0.05). Based on the
Shapiro and Wilk (1965) statistic, the residuals for both models
were normally distributed (a ¼ 0.05). The predicted heights for
both species are plotted in Figure 1. The model fits are good.
The models that were fit without climate variables resulted in
poorer fits to the data. The AIC for the Taiwan incense-cedar
height model increased to 117.0 from 106.9 and the error variance
increased to 0.2234 from 0.1754. For the taiwania height model,
the AIC went from 20.6 to 31.6 and the error variance went from
0.01791 to 0.08275. The non-climate-based models for Taiwan
incense-cedar and taiwania are, respectively:
h = (26.3981 + u) × (1 − e−0.02843×t )a2
h = h0 + (0.6548 + u) × (t − t0 )
Climate/height growth relationships for Taiwania and Calocedrus
Figure 2 Climate variables MST (a), MSP (b) and GDD (c) and their trend line plotted against year for the Taiwan incense-cedar data (Lianhuachih climate
station) and the taiwania data (Lioukuei climate station). Data used in the analyses range from 1961 to 2007 for Taiwan incense-cedar and from 1981 to
1996 for taiwania.
where all variables are as described for the full models,
a2 =
ln(h0 /(26.3981 + u))
,
ln(1 − e−0.02843×t0 )
and the variances for the random effect u are 0.8354 for the Taiwania incense-cedar model and 0.01512 for the taiwania model.
The mean annual temperature and annual precipitation at the
Lianhuachih climate station were 20.88C and 2295 mm, respectively, and were 18.68C and 2200 mm at the Lioukuei weather station.
The data for MST, MSP and GDD are shown in Figure 2 along with
their trend lines fitted by linear regression. There are no long-term
trends in the data except for a downward trend for MST at the Lioukuei climate station (taiwania data). MST at this climate station is
decreasing by 0.668C per decade. The variability in precipitation
appears to be increasing after year 2000. Since there is no trend in
most of the data, the year-to-year variability in climate is critical
for correlating periodic tree height growth with climate.
The endpoints for the climate variables in the simulation
scenarios are given in Table 4. Figure 3 shows the height trajectories
for the simulations.
Discussion
This research quantifies the effect that climate has on the height
growth of Taiwan incense-cedar and taiwania. The climate variables
that were most likely closely linked to growth were identified as being
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Table 4 Climate values used in the simulations to analyse the effects of
climate on the height growth models
Species
Climate
MST
MSP
GDD
Taiwan incense-cedar
Average
Cold/dry
Cold/wet
Hot/dry
Hot/wet
A1B
Average
Cold/dry
Cold/wet
Hot/dry
Hot/wet
A1B
22.34
21.99
22.08
25.33
26.07
24.34
24.84
24.61
24.27
26.13
27.51
26.84
2102
1130
4138
1864
2602
2522
2632
1020
4312
1568
3033
3158
N/A
N/A
N/A
N/A
N/A
N/A
6938
6839
6673
7242
7168
7113
Taiwania
N/A, not applicable.
MSTand MSP for Taiwan incense-cedar and MST, MSPand GDD for taiwania. Other climate variables are related to the height growth of
these species as well. However, given the high degree of correlation
between many of the climate variables, these three variables were
considered to be the most biologically relevant from the set of variables under consideration.
The projection form of the models results in dynamic models. That
is, the models can project a known height to obtain a predicted height
at some other time. This predicted height can then be further projected for another period of time. This is opposed to static regression
models where the response variable is predicted rather than projected. The projection form of the models has the advantage that
the parameters can be updated over each projection period. Under
a constant climate, the parameters of the model would also be constant and a simple height prediction model could be developed, as is
done with site index models. However, with a changing climate, the
projection form with parameters predicted from climate variables
allows the parameters to be updated (and hence height growth trajectories) as the climate changes. Height projections should be made
in lockstep with the climate changes to ensure that the climatebased model parameters remain relevant to the prevailing climate.
Creating a dynamic model from a static model by changing the
value of a variable (e.g. allow site index to change as the climate
changes) creates a new set of issues that must then be addressed,
namely that the height projections are not smooth (they will form
a sawtooth profile when site index changes). The sawtooth profile
is avoided in the projection model because projections are always
made starting from a known (or predicted) point.
These models should be calibrated to obtain local predictions
(Jiang and Li, 2010; Sirkiä et al., 2015). Calibration involves predicting the value of the random effect u in the above models for a specific tree or plot based on available data. Therefore, two or more
height observations at different ages are required to fully specify
the model: one observation to provide a value for h0 and t0 and
the other observation(s) to predict the value of the random effect.
Trees exhibit either determinate or indeterminate growth.
Whether a species exhibits determinate or indeterminate growth
has implications when incorporating climate into a dynamic
height growth model, such as the one described here. Shoot
growth for determinate species (e.g. Pinus and Picea) results from
370
Figure 3 Height trajectories for Taiwan incense-cedar (a) and taiwania (b)
for different climate scenarios.
the expansion of a terminal bud that has been performed in the
previous year. Consequently, the temperature at the time of
bud formation influences the height growth in the following year
(Kozlowski and Keller, 1966; Zimmerman and Brown, 1971).
Shoot growth for species with indeterminate growth are more dependent on current year photosynthate production (Kozlowski and
Clausen, 1966; Kozlowski and Keller, 1966). Hence, height growth is
correlated to current year growing conditions and is essentially a
continuous process when the environmental conditions are favourable for growth (Harry, 1987). Therefore, current year climate
variables are important predictors in an annual height growth
Climate/height growth relationships for Taiwania and Calocedrus
model for indeterminant species, whereas current and previous
year climate variables are important predictors for determinant
species. Species in the Cupressaceae family, of which both taiwania
and Taiwan incense-cedar are members, have indeterminate
growth (Zobel, 1983; Harry, 1987; Parker and Johnson, 1987;
Morgenstern, 1996; Chung and Kuo, 2005).
The parameters of the height models define the trajectory of predicted height growth. For the Chapman–Richards model formulation (Taiwan incense-cedar), parameter a0 is the asymptote, a1 is
the rate parameter and a2 is the shape parameter (Sharma and
Parton, 2007). Parameter a1 in the linear model for taiwania is the
height growth rate. The model for Taiwan incense-cedar is hard to
interpret because the parameters themselves are functions of
climate variables, which are correlated to each other. For the taiwania model, height growth will decrease with increasing precipitation,
given a constant MST and GDD. However, the interaction between
MST and GDD makes it difficult to make general statements about
the model behaviour as these variables change. A simulation and
graphical approach was employed to assist in examining the
effect that climate has on height growth of both species. In practice,
none of the scenarios in these simulations will be realized; hence,
these interpretations are more illustrative rather than definitive.
The following discussion is based on the height trajectories shown
in Figure 3. The response to climate appears to be slight for taiwania
when compared with Taiwan incense-cedar. However, this is due to
the scale of the age axis in the figure. The heights at age 25 for taiwania ranged from 19.17 to 21.17 m and they ranged from 12.96 to
13.85 m for Taiwan incense-cedar. Therefore, the response was
greater for taiwania than for Taiwan incense-cedar, although this
conclusion is based on the climate scenarios used in the simulations.
For Taiwan incense-cedar, the cold/wet and A1B scenarios resulted in
a decrease in height growth compared with the current average,
whereas height growth increased under the other scenarios. The
dry scenarios led to increased height growth and precipitation had
more of an effect on height growth for the cold scenario than for
the hot scenario. For taiwania, the cold scenarios produced slightly
poorer height growth than the current average climate scenario,
and the warmer scenarios, including the A1B scenario, all predicted
an increase in height growth over the average.
This research provides information on the effect that a changing
climate may have on height growth of taiwania and Taiwan incensecedar. Better informed decisions on the conservation and stewardship of these species can be made by considering the effect of
climate on their growth. Identifying sites for these species based
on climate suitability would assist in habitat conservation. Growth
information would guide harvesting operations to ensure that any
harvesting is done sustainably. Other management activities
where height/climate relationships might be considered are an
increased planting programme, identifying populations that might
be better adapted to future climates, assisted migration of these
populations and breeding programmes for trees that are better
adapted to the expected future climate. Coupling survival/climate
information for these two species with the growth information
would provide an even more powerful tool for conservation and
good stewardship. The relationship between tree mortality and
climate is an important potential future research topic.
The sample for this research was limited in size and geographic
range. Therefore, the height growth models for both species should
not be extrapolated beyond the climate and age range of the data
as unreasonable predicted height growth trajectories could result.
While both models would benefit from more data, additional data
for the taiwania model would be especially beneficial since the age
range for the data is very limited. A potential source of data is a
system of permanent sample plots in natural and managed
stands across Taiwan. These plots were established to monitor
tree growth. The monitoring plots containing taiwania and
Taiwan incense-cedar would need to be identified and coupled
with climate data. This would provide a source of data to validate
the height models under a future changing climate and potentially
provide additional data for model fitting.
The approach taken in this research is to model the correlations
between periodic growth and climate. Other analytical techniques
involve searching for correlations between long-term growth (e.g.
site index) and average climate (e.g. Kim et al., 2014; Sharma et al.,
2015). Both approaches are valid. One advantage of the approach
taken here is that differences in site productivity are accounted for
by the use of prior knowledge via the variables h0 and t0, to create
a dynamic model. These variables act like site index and serve as a
proxy for all the site factors that influenced tree height growth up
to age t0, leaving only climate to influence growth over the next
period. Site factors that influence tree growth such as soil nutrient
levels are implicitly included in the analysis. When growth is predicted
only with climate variables, or through models that predict site index
from climate, these non-climatic site factors are not accounted for
in the models, rendering them potentially less accurate than the
approach that was taken here.
Good climate data for test sites are scarce. Most climate/growth
studies are retrospective using stem analysis techniques or permanent plot data. Unless a climate station was located near to the test
site, good climate data will be lacking. To get around this issue,
researchers often use climate models to predict climate data. In
this case, it is essential that the climate model is accurate to get interpretable results that are reliable. Given the small variations in
temperature observed in this study, an error of, for example, 18C in
predicted temperature is quite large. Furthermore, when predicted
climate data are used as input into a growth model such as the
ones developed here, the growth model then becomes calibrated
specifically to that data source. Using real data, or data from a different climate model, or even data from a different version of the
climate model, may result in errors in the growth model. Another potential issue with using data from climate models (and models in
general) is that some variability in the data has been eliminated.
For climate models that predict long-term trends, the year-to-year
variability has been eliminated. The development of the dynamic
models was possible because short-term variability in climate
could be correlated with short-term variability in height growth.
This would not have been possible with long-term trend climate data.
Summary and conclusions
This research quantifies the effect of climate on the height growth
of Taiwan incense-cedar and taiwania. Mean summer temperature
and mean summer precipitation are important predictors of height
growth for Taiwan incense-cedar. These variables, along with
growing degree-days, are important predictors of height growth
for taiwania. The dynamic height growth models that were developed can be used to predict height growth under a changing
climate. Height growth is expected to decrease for Taiwan incensecedar and increase for taiwania under the A1B climate change
scenario. The management and conservation of these species
371
Forestry
will be aided with the information on the relationship between
climate and growth afforded by the model described herein.
Li, C.-F., Chytrý, M., Zelený, D., Chen, M.-Y., Chen, T.-Y., Chiou, C.-R. et al. 2013
Classification of Taiwan forest vegetation. Appl. Veg. Sci. 16, 698– 719.
Acknowledgements
Lin, L.-Y., Chen, Y.-M., Chu, J.-L., Liu, P.-L., Lee, H.-L. and Huang, Y.-C. 2013
Introduction to the Taiwan Climate Change Projection and Information
Platform Project. http://www.apectyphoon.org/sdt175/img/img/3863/
Newsletter_September_2013/6._Global_Aspect_Chu.pdf (accessed on 19
June, 2015).
We thank Peter Ott of the British Columbia Ministry of Forests, Lands and
Natural Resource Operations for review comments on an early draft. We
also thank two anonymous reviewers and Mark Ducey, the editor, for
good suggestions that greatly improved this manuscript.
Conflict of interest statement
None declared.
References
Central Weather Bureau. 2015 Weather Phenomena. http://www.cwb.gov.
tw/V7e/knowledge/encyclopedia/me025.htm (accessed on 17 June,
2015).
Chang, C.-T., Lin, C.-T., Wang, S.-F. and Vadeboncoeur, M.A. 2011 Assessing
growing season beginning and end dates and their relation to climate in
Taiwan using satellite data. Int. J. Remote Sens. 32, 5035–5058.
Mailly, D.D., Turbis, S., Auger, I. and Pothier, D. 2004 The influence of site tree
selection method on site index determination and yield prediction in black
spruce stands in northeastern Québec. For. Chron. 80, 134–140.
Mäkinen, H., Verkasalo, E. and Tuimala, A. 2014 Effects of pruning in Norway
spruce on tree growth and grading of sawn boards in Finland. Forestry 87,
417–424.
Meldahl, R.S., Kush, J.S., Rayamajhi, J.N. and Farrar, R.M. Jr 1998 Productivity of
natural stands of longleaf pine in relation to competition and climatic factors.
In The Productivity and Sustainability of Southern Forest Ecosystems in a
Changing Environment. Mickler, R.A. and Fox, S. (eds). Springer-Verlag,
pp. 231–254.
Morgenstern, E.K. 1996 Geographic Variation in Forest Trees: Genetic Basis
and Application of Knowledge in Silviculture. UBC Press, 209 pp.
Newberry, J.D. 1991 A note on Carmean’s estimate of height from stem
analysis data. For. Sci. 37, 368– 369.
Chiu, C.-M., Chien, C.-T. and Nigh, G. 2015 A comparison of 3 taper equation
formulations and an analysis of the slenderness coefficient for Taiwan
incense-cedar (Calocedrus formosana). Aust. For. 78, 159– 168.
Nishizono, T. 2010 Effects of thinning level and site productivity on
age-related changes in stand volume growth can be explained by a single
rescaled growth curve. For. Ecol. Manage. 259, 2276– 2291.
Chung, J.-D. and Kuo, S.-R. 2005 Reproductive cycle of Calocedrus
formosana. Taiwan J. For. Sci. 20, 315– 329.
Parker, T. and Johnson, F.D. 1987 Branching and terminal growth of western
redcedar. Northwest Sci. 61, 7 –12.
Council for Economic Planning and Development. 2012 Adaptation Strategy
to Climate Change in Taiwan. http://www.ndc.gov.tw/en/cp.aspx?n=
97B9027210DBD173 (accessed on 18 August, 2015).
Pienaar, L.V. and Turnbull, K.J. 1973 The Chapman-Richards generalization
of von Bertalanffy’s growth model for basal area growth and yield in
even-aged stands. For. Sci. 19, 2 –22.
Davidian, M. and Giltinan, D.M. 1995 Nonlinear Models for Repeated
Measurement Data. Chapman & Hall, 359 pp.
Pokharel, B. and Froese, R.E. 2009 Representing site productivity in the basal
area increment model for FVS-Ontario. For. Ecol. Manage. 258, 657–666.
Guan, B.-T., Chung, C.-H., Lin, S.-T. and Shen, C.-W. 2009 Quantifying height
growth and monthly growing degree days relationship of plantation Taiwan
spruce. For. Ecol. Manage. 257, 2270 –2276.
Richards, F.J. 1959 A flexible growth function for empirical use. J. Exp. Bot.
10, 290– 300.
Hann, D.W. and Scrivani, J.A. 1987 Dominant-height-growth and Site-index
Equations for Douglas-fir and Ponderosa Pine in Southwest Oregon. Research
Bulletin 59. Oregon State University.
Sen, A. and Srivastava, M. 1990 Regression Analysis: Theory, Methods, and
Applications. Springer-Verlag, 347 pp.
SAS Institute Inc. 2011 SAS OnlineDocw 9.3. SAS Institute Inc.
Harry, D.E. 1987 Shoot elongation and growth plasticity in incense-cedar.
Can. J. For. Res. 17, 484– 489.
Shapiro, S.S. and Wilk, M.B. 1965 An analysis of variance test for normality
(complete samples). Biometrika 52, 591– 611.
Hsu, H.-H., Chou, C., Wu, Y.-C., Lu, M.-M., Chen, C.-T. and Chen, Y.-M. 2011
Climate Change in Taiwan: Scientific Report 2011 (summary). http://tccip.
ncdr.nat.gov.tw/v2/upload/book/20150410100030.pdf (accessed on 18
September, 2015).
Sharma, M. and Parton, J. 2007 Height-diameter equations for boreal tree
species in Ontario using a mixed-effects modelling approach. For. Ecol.
Manage. 249, 187– 198.
Intergovernmental Panel on Climate Change. 2000 Emissions Scenarios
Summary for Policymakers. https://www.ipcc.ch/pdf/special-reports/spm/
sres-en.pdf (accessed on 19 June, 2015).
Jiang, L. and Li, Y. 2010 Application of nonlinear mixed-effects modeling
approach in tree height prediction. J. Comput. 5, 1575–1581.
Kim, D.-H., Kim, H., Kim, E.-G. and Seok, H.-D. 2014 Analysis of the effect of
climate change on site index of Korean white pine. For. Sci. Technol. 10, 73–79.
Kozlowski, T.T. and Clausen, J.J. 1966 Shoot growth characteristics of
heterophyllous woody plants. Can. J. Bot. 44, 827– 843.
Sharma, M., Subedi, N., Ter-Mikaelian, M. and Parton, J. 2015 Modeling
climatic effects on stand height/site index of plantation-grown jack pine
and black spruce trees. For. Sci. 61, 25 –34.
Sirkiä, S., Heinonen, J., Miina, J. and Eerikäinen, K. 2015 Subject-specific
prediction using a nonlinear mixed model: consequences of different
approaches. For. Sci. 61, 205–212.
Thomas, P. and Farjon, A. 2011 The IUCN Red List of Threatened Species
Version 2015.1 Taiwania cryptomerioides. http://www.iucnredlist.org/
details/31255/0 (accessed on 18 June, 2015).
Kozlowski, T.T. and Keller, T. 1966 Food relations of woody plants. Bot. Rev.
32, 293– 382.
Yang, Y., Farjon, A. and Liao, W. 2013 The IUCN Red List of Threatened Species
Version 2015.1 Calocedrus formosana. http://www.iucnredlist.org/details/
31254/0 (accessed on 18 June, 2015).
Kutner, M.H., Nachtsheim, C.J., Neter, J. and Li, W. 2005 Applied Linear
Statistical Models. McGraw-Hill Irwin, 1396 pp.
Zimmerman, M.H. and Brown, C.L. 1971 Trees Structure and Function.
Springer-Verlag, 336 pp.
Landsberg, J.J. 1986 Physiological Ecology of Forest Production. Academic
Press, 198 pp.
Zobel, D.B. 1983 Twig elongation patterns of Chamaecyparis lawsoniana.
Bot. Gaz. 144, 92 –103.
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