JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, G01030, doi:10.1029/2011JG001868, 2012
Uncertainties in terrestrial carbon budgets related
to spring phenology
Su-Jong Jeong,1 David Medvigy,1 Elena Shevliakova,2,3 and Sergey Malyshev2,3
Received 20 September 2011; revised 4 January 2012; accepted 6 January 2012; published 8 March 2012.
[1] In temperate regions, the budburst date of deciduous trees is mainly regulated by
temperature variation, but the exact nature of the temperature dependence has been a matter
of debate. One hypothesis is that budburst date depends purely on the accumulation of
warm temperature; a competing hypothesis states that exposure to cold temperatures is also
important for budburst. In this study, variability in budburst is evaluated using 15 years
of budburst data for 17 tree species at Harvard Forest. We compare two budburst
hypotheses through reversible jump Markov chain Monte Carlo. We then investigate
how uncertainties in budburst date mapped onto uncertainties in ecosystem carbon using
the Geophysical Fluid Dynamics Laboratory’s LM3 land model. For 15 of 17 species,
we find that more complicated budburst models that account for a chilling period are
favored over simpler models that do not include such dependence. LM3 simulations
show that the choice of budburst model induces differences in the timing of carbon
uptake commencement of 11 days, in the magnitude of April–May carbon uptake of
1.03 g C m2 day1, and in total ecosystem carbon stocks of 2 kg C m2. While
the choice of whether to include a chilling period in the budburst model strongly
contributes to this variability, another important factor is how the species-dependent
field data gets mapped onto LM3’s single deciduous plant functional type (PFT). We
conclude budburst timing has a strong impact on simulated CO2 fluxes, and uncertainty
in the fluxes can be substantially reduced by improving the model’s representation of
PFT diversity.
Citation: Jeong, S.-J., D. Medvigy, E. Shevliakova, and S. Malyshev (2012), Uncertainties in terrestrial carbon budgets related
to spring phenology, J. Geophys. Res., 117, G01030, doi:10.1029/2011JG001868.
1. Introduction
[2] Phenology is the study of the timing of recurring seasonal biological events of terrestrial ecosystems [Schwartz,
1998]. Spring leaf budburst is recognized as being sensitive to climate variations, and is thus a crucial factor for
predicting the dynamic responses of the terrestrial ecosystem
to climate change [Menzel and Fabian, 1999; Schwartz et al.,
2006; Richardson et al., 2006; Jeong et al., 2011]. Furthermore, variations in the timing of leaf budburst also affect
changes in climate since they affect spatiotemporal dynamics
of surface radiation, temperature, the hydrological cycle, and
the terrestrial carbon cycle [Baldocchi et al., 2005; Bonan,
2008; Jeong et al., 2009a, 2009b, 2010; Richardson et al.,
2010a]. For example, in deciduous forests, the transition
from dormancy to leaf maturity can cause an increase in
1
Atmospheric and Oceanic Sciences Program, Department of
Geosciences, Princeton University, Princeton, New Jersey, USA.
2
Department of Ecology and Evolutionary Biology, Princeton
University, Princeton, New Jersey, USA.
3
Geophysical Fluid Dynamics Laboratory, NOAA, Princeton, New
Jersey, USA.
Copyright 2012 by the American Geophysical Union.
0148-0227/12/2011JG001868
latent heat flux by enabling transpiration and a decrease in
atmospheric CO2 concentrations by enabling plant carbon
uptake. Thus, realistic simulation of the timing of budburst is
important for improving our understanding of the carbon and
water cycles in the climate system.
[3] The date of budburst is generally thought to be determined by various climatic factors, including temperature,
photoperiod, precipitation, soil moisture, and evaporation
[Murray et al., 1989; Menzel and Fabian, 1999; Baldocchi
et al., 2005]. In temperate climates, temperature is the most
important factor controlling budburst [Menzel and Fabian,
1999], and several previous studies have utilized processbased spring phenology models that represent budburst as
a function of temperature [Cannell and Smith, 1983;
Lechowicz, 1984; Murray et al., 1989; Chuine and Cour,
1999; Baldocchi et al., 2005; Schwartz and Hanes, 2010a].
Budburst is commonly prescribed to occur when the sum
of daily mean temperature above a given threshold (i.e.,
growing degree days or GDD) accumulated from a certain
starting day reaches a predetermined value [Cannell and
Smith, 1983; Lechowicz, 1984]. However, it has also
been argued that some tree species in temperate regions
also require a certain amount of exposure to cold temperatures in order to break their dormancy [Murray et al.,
G01030
1 of 17
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
Table 1. Mean and Standard Deviations (STD) of Budburst Date
of 17 Woody Species in Harvard Forest
Latin Binomial
Common Name
Canopy
Potential
Prunus serotina
Cornus alternifolia
Populus tremuloides
Amelanchier canadensis
Crataegus sp.
Betula papyrifera
Hamamelis virginiana
Acer saccharum
Acer pensylvanicum
Acer rubrum
Betula alleghaniensis
Betula lenta
Fagus grandifolia
Quercus rubra
Fraxinus americana
Quercus velutina
Quercus alba
Species-average
Black cherry
Alt-leaf dogwood
Trembling aspen
Shadbush
Hawthorn
Paper birch
Witch hazel
Sugar maple
Striped maple
Red maple
Yellow birch
Black birch
American beech
Red oak
White ash
Black oak
White oak
over
under
over
under
under
over
under
over
under
over
over
over
over
over
over
over
over
Mean
STD
111
118
119
122
123
124
124
124
127
128
128
129
129
129
132
134
136
126
3.8
6.0
6.2
5.1
5.0
5.4
5.0
4.9
5.7
4.7
5.9
6.8
4.1
5.1
5.9
6.0
6.4
6.2
1989; Chuine, 2000; Baldocchi and Wong, 2008; Schwartz
and Hanes, 2010a]. This raises the possibility that insufficient winter chilling under climatic warming may lead to
later budburst.
[4] Accordingly, process-based budburst models have
been divided into two dominant groups: simple thermal
forcing models (GDD models) and thermal forcing models
that include a chilling requirement (GDD plus chilling
models). Although many previous studies compared the two
kinds of models [Chuine, 2000; Chiang and Brown, 2007;
Hänninen and Kramer, 2007; Richardson and O’Keefe,
2009], there is no general consensus on which model is
more realistic. Comparing two studies of tree budburst at
Harvard Forest brings this problem into perspective.
Richardson and O’Keefe [2009] investigated a variety of
budburst models of varying complexity, including GDD
models and GDD plus chilling models. Overall, they found
that GDD models were best for 13 of 33 species, and that
GDD plus chilling models were best for 20 of 33 species.
Even for the 20 species for which a GDD model was not
optimal, they argued that it would still be a reasonable
choice. In contrast, Chiang and Brown [2007] argued that a
3-parameter GDD plus chilling model best suited the
observations for all 17 species. The level of confidence to be
ascribed to this result was not specified. In addition, both
previous studies have focused only on a single best parameter set for a given budburst model and have not typically
provided information on uncertainties and covariances of
budburst model parameters.
[5] These results suggest several avenues for further
investigation. First, to address the uncertainty as to whether
Harvard Forest tree species actually do have a chill
requirement, it would be useful to develop a method of
quantifying our confidence in different budburst hypotheses.
Most previous studies carried out of regressions between
simulated and observed budburst dates and compared the
resulting r2 values [Chuine, 2000; Richardson et al., 2006;
Chiang and Brown, 2007; Hänninen and Kramer, 2007].
This method does not offer any protection against overfitting, and it is also difficult to extract the relative support
G01030
for different models. A different approach was taken by
Richardson and O’Keefe [2009], who used Akaike’s
Information Criterion (AIC) to select the best model for
budburst. AIC takes into account goodness-of-fit, but also
penalizes complicated models with many tunable parameters
[Akaike, 1973]. However, the AIC still does not provide a
metric for how strongly one model should be preferred to
another [Sambridge et al., 2006]. A second avenue for
investigation pertains to evaluation of terrestrial biosphere
model uncertainties resulting from uncertainties in budburst.
Budburst uncertainties lead to uncertainties in simulated
terrestrial carbon budgets and potentially ecosystem composition and structure, but this has not been quantified in previous studies.
[6] The specific objectives in the present study are to (1)
quantify the levels of support of different budburst hypotheses; (2) estimate the parameter uncertainties in budburst
models; (3) estimate the sensitivities of seasonal and century
scale terrestrial carbon budgets to uncertainties in budburst
hypothesis and parameter selection. We focus on Harvard
Forest (42.532°N, 72.188°W) because of its rich, long-term
(15 years), and species-specific phenology records [O’Keefe,
2000]. In section 2, data and model used in this study are
shown. In section 3, details in the method of hypothesis
testing are described. In section 4, budburst hypothesis and
sensitivity of terrestrial carbon budgets to budburst are
evaluated. In section 5, results in the present study are
discussed.
2. Data and Model
2.1. Budburst Data
[7] In Harvard Forest, located in central Massachusetts,
spring budburst dates of 33 woody species have been
recorded at 3–7 day intervals from April through June from
1990 to the present [O’Keefe, 2000]. These records are one
of the longest budburst records in the world and have been
used in various ecology and climate studies [Jolly et al.,
2005; Chiang and Brown, 2007; Richardson and O’Keefe,
2009; Schwartz and Hanes, 2010b]. These trees are distributed within 1.5 km of the Harvard Forest headquarters at
elevations between 335 and 365 m. We focused on 17 of the
33 woody species whose budburst records are particularly
Figure 1. Time series of mean and standard error of budburst date for 5 individual Acer rubrum trees at Harvard
Forest.
2 of 17
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
G01030
generally called a thermal forcing or spring warming model
(e.g., GDD model). GDD is defined by:
GDDðtÞ ¼
t
X
maxðT 5-C; 0Þ;
ð1Þ
Jan 1
and budburst is predicted to occur when
GDDðt Þ > GDDthreshold :
Figure 2. Time series of budburst distributions for 17 species at Harvard Forest.
long, spanning the period 1992–2005 (Table 1). Speciesaverage in Table 1 refers to the average budburst date of the
17 species. In this data set, the time of the budburst is
defined as date when 50% of the buds on the individual tree
have recognizable leaves emerging from them.
[8] The budburst date of each species is usually obtained
by evaluating 3 to 5 individual trees (which vary from year
to year) in each species. The intraspecies mean and variability is presented in Figure 1 for Acer rubrum (n = 5 in
each year), which comprises more basal area than any other
species at Harvard Forest. There is no significant trend in the
mean, and a typical value for the within-year standard
deviation (STD) is about 5 days. Similar intraspecies variations are commonly observed in the other 16 species (not
shown).
[9] To illustrate the interspecies variability, we first
defined a representative budburst date for each species by
averaging over the individuals of each species in each year,
in accord with previous studies [Chiang and Brown, 2007;
Richardson and O’Keefe, 2009; Schwartz and Hanes,
2010b]. The variation of the species-representative budburst dates are shown in Figure 2. There are no significant
trends, and the degree of interspecies variability ranges from
2 to 10 days depending on the year. Comparing Figures 1
and 2, the intraspecies variability is comparable to the
interspecies variability. In terms of interannual variations of
STD, the highest and lowest STD of interspecies and intraspecies are observed at the same year (in 2002 for the
highest STD and in 2001 for the lowest STD).
[10] We also used budburst data from the University of
Wisconsin–Milwaukee (UWM) field station (43.4°N,
88.0°W) [Schwartz and Hanes, 2010b]. For this site,
budburst data were available from 2000 to 2009. The
criteria for budburst at the UWM site were the same as
the Harvard Forest criteria. For four species (Quercus
rubra, Betula papyrifera, Fraxinus americana, and Cornus
alternifolia), there were budburst observations at both
sites.
2.2. Budburst Parameterizations
[11] We have focused on two main hypotheses for the
climate drivers of budburst. The first hypothesis is that
budburst responds solely to accumulating heat units. This is
ð2Þ
Here, T is the daily mean temperature and GDDthreshold is the
single model parameter. Summation in equation (1) begins
on January 1. This simple GDD model is used in wellknown terrestrial models such as the Integrated Biosphere
Simulator (IBIS) [Foley et al., 1996] and the Community
Land Model–Dynamic Global Vegetation Model (CLMDGVM) [Levis et al., 2004]. Both of these models assume
that the leaves appear when GDD (t) exceeds a GDDthreshold
equal to 100. In the present study, we refer to equation (2) as
a spring warming (W) model.
[12] The second hypothesis is that budburst also has some
chilling requirement. This model assumes that chill days
reduce the GDD requirement, and predicts that budburst
occurs when
GDDðtÞ ≥ a þ b expðc NCDðtÞÞ; with c < 0;
ð3Þ
where GDD (t) is again defined by equation (1). NCD is
defined as the number of chilling days (any day with daily
mean temperature less than 5°C constitutes a chilling day)
from Jan 1. a, b, and c are the three model parameters. This
type of model is used in the ORganizing Carbon and
Hydrology in Dynamic EcosystEms (ORCHIDEE) model
[Krinner et al., 2005] and the Spatially Explicit Individual
Based–Dynamic Global Vegetation Model (SEIB-DGVM)
[Sato et al., 2007]. ORCHIDEE and SEIB-DGVM both
adopt the budburst parameters from Botta et al. [2000] (a =
68, b = 638, and c = 0.01). Thus, we refer to equation (3)
as chilling and spring warming (CW) model. Figure 3 shows
sample history of daily GDD, NCD, and thermal criteria for
budburst (e.g., right hand of equation (3)).
Figure 3. Sample history of daily growing degree days
(GDD), number of accumulated chill days (NCD), and thermal criteria for the budburst (e.g., right hand of equation (3)).
3 of 17
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
[13] In this study, we use the common approach of
assigning a baseline temperature of 5°C for calculating GDD
and NCD, and of accumulating both GDD and NCD from
January 1st. Although some previous studies suggested
somewhat different choices for the definition of GDD and
NCD, it has not been shown that one choice is markedly
better than any other [Hunter and Lechowicz, 1992; Botta
et al., 2000].
2.3. LM3 Model
[14] The model consists of two main components: a land
surface model and a global dynamic vegetation model
[Shevliakova et al., 2009]. Vegetation is represented by a
combination of five C pools: leaves, fine roots, sapwood,
heartwood (hereafter simply wood), and labile carbon stores.
The sizes of all pools are modified daily, depending on
amounts of C accumulated in the biophysics model, and
according to a set of allocation rules. Carbon lost from
vegetation pools is deposited into two soil C pools. The
model simulates changes in the C pools of vegetation caused
by phenological processes (e.g., leaf drop and emergence),
natural mortality, and fire. The current version of LM3 calculates annual loss of carbon due to fire as proportional to
fuel available and the number of drought months.
[15] The five vegetation types are combinations of three
characteristics: physiology (i.e., C3 versus C4), leaf longevity (i.e., temperate versus tropical broadleaf versus cold
evergreen), and allocation ratios among stems, roots, and
leaves (i.e., tree versus grass). All tree vegetation types have
C3 physiology. The phenology of deciduous plants is governed by monthly environmental triggers and is based on the
phenology of ED model [Moorcroft et al., 2001; Medvigy
et al., 2009]. Leaves and fine roots are dropped or become
dormant when one of the two conditions is met: the mean
monthly canopy air temperature drops below 10°C or the
mean monthly plant-available soil water in the root zone
falls to less than 10% of its maximum possible value.
[16] The land surface model operates on 30 min fast time
step and includes canopy biophysics, ecosystem CO2
exchange, soil/snow thermodynamics and hydrology, and
radiation exchange. Among new hydrological features are
frozen soil dynamics, a parameterization of water table
height, and groundwater discharge to streams derived from
groundwater-hydraulic assumptions and surface topographic
information (P. C. D. Milly et al., “Enhanced representation
of land physics for Earth-system modeling,” in preparation).
model hypotheses and in the selection of model parameters.
For a given model hypothesis, many techniques are available
to estimate appropriate parameter values [Trudinger et al.,
2007; Fox et al., 2009]. In particular, standard Markov
chain Monte Carlo (MCMC) has now been used to estimate
parameters for numerous terrestrial biosphere models [e.g.,
Reichstein et al., 2003; Knorr and Kattge, 2005; Wang et al.,
2007; Moore et al., 2008; Richardson et al., 2010b]. However, in order to evaluate different model hypotheses, a more
general technique must be used. This is exactly the program
of RJMCMC: to determine the hypothesis best supported by
the data, while also penalizing more complicated hypotheses.
[18] RJMCMC is useful when one has to choose between
different models. The models may or may not have the same
number of parameters. A principal benefit of RJMCMC is
that it assigns a quantitative posterior probability to models
themselves, and not just to model parameters. For example,
if the RJMCMC assigned a probability of 99.9% to one
model and a probability of 0.1% to a second model, we
might reasonably exclude the second model from further
consideration. However, if the probability associated with
one model was 50.1% and the probability associated with
the second model was 49.9%, we probably would not want
to exclude either model. RJMCMC thus differs from commonly used information criteria like the Akaike Information
Criterion or the Bayesian Information Criterion. These
information criteria only state whether one model should be
preferred to another; they say nothing about the margin of
preference. In the remainder of this section, we describe how
we apply RJMCMC to our phenology analysis. Mathematical details of RJMCMC are given in Appendices A and B.
3.1. RJMCMC for the Budburst Hypotheses Analysis
[19] In this section, we describe the priors and the likelihood function used in our RJMCMC analysis of budburst.
Technical details on the implementation of RJMCMC specific to this problem can be found in Appendix B. We
specify the prior PDF on the phenology model, P(x), in two
different ways. The first is based on the work of Botta et al.
[2000], who carried out a global-scale calibration using
satellite observations. They reported the best estimates and
uncertainties for the three parameters of equation (3), but did
not provide any covariance information. For our first choice
of prior (P1(x)), we assume that these results are applicable
to Harvard Forest and take the following form:
P1 ðxÞ ¼
3. Hypothesis Testing by Reversible Jump
Markov Chain Monte Carlo
[17] This section describes how we will assign relative
levels of support to different budburst models. Our approach
is to use reversible jump Markov chain Monte Carlo
(RJMCMC) [Green, 1995]. RJMCMC has not previously
been used in the context of terrestrial biosphere modeling,
and it has only recently started appearing the Earth Sciences
literature [Sambridge et al., 2006; Hopcroft et al., 2009;
Bodin et al., 2009]. The method is predicated on the observation that numerical models, including terrestrial biosphere
models, consist of a set of hypotheses cast into the form of
mathematical equations that typically include empirical
parameters. Uncertainty arises both in the formulation of the
G01030
1
ð2pÞ3=2
1
1
exp ðx xB ÞT SB1 ðx xB Þ
2
jSB j
ð4Þ
where xB = (68, 638, 0.01). The three elements of this
vector correspond to a, b, and c, respectively, of equation
(3). The covariance matrix SB is given by: diag(484, 256,
1 106). Because Botta’s parameter estimates and uncertainties were derived from large-scale remote sensing and
may not be appropriate for the local ecosystem at Harvard
Forest, we defined a second prior, P2(x), consisting of a
uniform distribution U:
P2 ðxÞ ¼ U xBlow ; xBhigh
ð5Þ
high
Here, xlow
= (300, 900, 0.09).
B = (150, 0, 0.01) and xB
This is a deliberately wide range that includes many
4 of 17
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
G01030
G01030
Table 2. Estimated Model Posterior Probabilities
Prior1 (Uniform)
Prior2 (Normal)
Common Name
W-Model
CW-Model
W-Model
CW-Model
Black cherry
Alt-leaf dogwood
Trembling aspen
Shadbush
Hawthorn
Paper birch
Witch hazel
Sugar maple
Striped maple
Red maple
Yellow birch
Black birch
American beech
Red oak
White ash
White oak
Black oak
Species-average
0.10
0.01
0.40
0.28
0.01
0.08
0.58
0.13
0.12
0.21
0.01
0.01
0.03
0.01
0.08
0.25
0.64
0.32
0.90
0.99
0.60
0.72
0.99
0.92
0.42
0.87
0.88
0.79
0.99
0.99
0.97
0.99
0.92
0.75
0.36
0.68
0.01
0.12
0.45
0.05
0.02
0.02
0.62
0.21
0.21
0.11
0.11
0.02
0.02
0.02
0.02
0.47
0.59
0.12
0.99
0.88
0.65
0.95
0.98
0.98
0.38
0.79
0.79
0.89
0.89
0.98
0.98
0.98
0.98
0.53
0.41
0.88
Figure 5. Posterior probability of model selections related
to the specified measurement error for Acer rubrum.
previously reported values [Botta et al., 2000; Richardson
et al., 2006; Fisher et al., 2007; Zhang et al., 2007].
[20] We assume that observational errors in the budburst
measurements are independent and normally distributed.
Thus, the likelihood function (see Appendix A) is assumed
to have the form of equation (A3). As a basis case, we take a
standard deviation of 3 days because the budburst dates were
recorded at 3–7 day intervals. However, to test the sensitivity of our results to this assumption, we also carried out
the RJMCMC algorithm with larger and smaller observational errors.
3.2. Model Calibration
[21] We used data from 1992 to 2001 for model calibration. Our baseline MCMC analyses consisted of 20,000
iterations for these years. The initial 4000 iterations were
discarded as a burn-in. After burn-in, we selected every fifth
sample (4000 samples from the last 16,000 iterations) to
represent the posterior PDF. We tested for convergence by
repeating the analysis using 60,000 (instead of 20,000)
iterations. We evaluated the model by using the 2002–2006
Harvard Forest data and the 2000–2009 UWM data.
4. Results
4.1. Evaluation of Budburst Hypotheses
[22] The posterior probabilities corresponding to the Wmodel and the CW-model for each species are shown in
Table 2. In prior 1 simulations, the posterior probability of
the W-model ranges from 0.01 to 0.64, whereas the posterior
probability of the CW-model ranges from 0.36 to 0.91.
Among the 17 species, 15 species show higher posterior
probability associated with the CW-model, whereas only 2
species show higher posterior probability associated with the
Figure 4. Sampling history for the selected model by RJMCMC simulations together with the histogram
of posterior probabilities for Acer rubrum.
5 of 17
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
Table 3. Summary of Optimized Parameters for Species for
Which the W-Model Had Higher Posterior Probability Than the
CW-Model
Mean (1s)
Common Name
Prior1
Prior2
Witch hazel
Black oak
116.3 (5.5)
163.6 (9.0)
116.0 (4.5)
163.9 (4.6)
W-model. When we increased the number of iterations (n)
by a factor of 3 to 60,000, the posterior probability has
shifted by less than 0.08 for all species. This small change
did not lead to a change in the mode of the PDF for any
species. This indicates that our default value of n = 20,000 is
sufficient for model selection.
[23] The results of the prior 2 simulations are qualitatively
similar to the results of prior 1 simulations. The selected
model in each species with prior 2 is same as the selected
model with prior 1, suggesting that the selection of the
optimal model for each species is not being dominated by
the prior information. Quantitatively, however, the posterior
probability of the CW-model in the prior 2 simulations is
much higher than that of the prior 1 simulations, regardless
of species. For the specific case of Acer rubrum, which is
one of dominant species at Harvard Forest, Figure 4 shows
the RJMCMC sampling history together with the histogram
of posterior probabilities. The higher acceptance rate of the
CW-model is clearly seen regardless of prior information.
Overall, the RJMCMC simulations suggest that 3-parameter
CW-model was well supported by the data for most of the
species regardless of prior information. These results indicate that the observed budburst date of many species is likely
influenced by chilling period. Higher posterior probability
associated with the W-model is only obtained for Hamamelis virginiana and Quercus velutina.
[24] We evaluated the sensitivity of model selection to the
specified measurement error, taking Acer rubrum as a case
study (Figure 5). The posterior probability of the CW-model
is markedly larger than that of the W-model for low levels of
observational error. With increases in observational error,
G01030
the posterior probability for the W-model increases. These
results suggest that if there are no observational errors in
budburst date, there is enough information in the observations to construct complicated models with large numbers of
parameters. Further, simulations with prior 2 are associated
with higher probabilities for the CW-model, indicating that
information from the prior can also lead to greater support
for more complex models. For the other 14 species for which
the CW-model has a higher posterior probability when the
observational error is 3 days, the support of the CW-model
relative to the W-model also decreases as observational error
increases. The other 2 species for which the W-model was
selected when observational error was 3 days (Hamamelis
virginiana and Quercus velutina) have shown similar features with CW-model dominant species. For example, with
increases in observational error, the posterior probability for
the CW-model increased. This indicates higher observation
errors can disturb the choice of optimal budburst in GDD
dominant species when the observational error is 3 days.
[25] The mean and standard deviation of the parameter
values were derived from the posterior distributions
(Tables 3 and 4). For example, Figure 6 shows the sampling
history for the parameter a in CW-model for Acer rubrum
and its posterior PDF for both assumptions on the prior. As
seen in the figure, the PDF of parameter a depends on prior
information. The parameter a using prior 1 is centered at
155, but it is centered at 156 using prior 2. The STD of
parameter a in the simulation with prior 1 has a larger
magnitude than the STD of parameter a in the simulation
with prior 2 (Tables 3 and 4). This larger STD is also clearly
seen in the sampling history for the parameter a in two different prior simulations (Figure 6). This suggests that prior
information played an essential role in constraining the
parameter value. These well-constrained features are also
observed in the other two parameters in the simulations with
prior 2. Furthermore, when we analyzed the other species,
the STD of each parameter was always smaller in the
RJMCMC with prior 2 than the RJMCMC with prior 1.
[26] To investigate the convergence of the RJMCMC,
additional simulations were run for 60,000 iterations. We
compared the mean values of a from the n = 20,000 and the
Table 4. Summary of Optimized Parameters for Species for Which the CW-Model Had Higher Posterior Probability Than the W-Model
Mean (1s)
Prior1
Common Name
Parameter a
Parameter b
Black cherry
Alt-leaf dogwood
Trembling aspen
Shadbush
Hawthorn
Paper birch
Sugar maple
Striped maple
Red maple
Yellow birch
Black birch
American beech
Red oak
White ash
White oak
Species-average
17.2 (14.1)
14.2 (8.0)
65.9 (25.9)
75.8 (10.4)
31.7 (25.9)
34.2 (28.2)
120.3 (33.4)
112.4 (17.6)
155.6 (10.1)
63.9 (22.0)
50.7 (28.5)
74.0 (25.9)
123.2 (27.7)
108.1 (25.5)
123.1 (33.5)
125.3 (30.4)
666.9 (128.1)
735.0 (346.0)
443.7 (211.0)
461.4 (168.5)
677.2 (175.9)
405.7 (185.7)
661.8 (289.4)
478.7 (295.9)
704.7 (194.9)
658.0 (187.3)
659.6 (153.5)
449.1 (146.9)
447.3 (273.1)
422.9 (162.3)
345.2 (177.8)
461.8 (209.4)
Prior2
Parameter c
0.031
0.025
0.034
0.034
0.024
0.018
0.012
0.042
0.014
0.022
0.021
0.010
0.037
0.024
0.020
0.012
(0.0051)
(0.0015)
(0.0097)
(0.0071)
(0.0050)
(0.0070)
(0.0184)
(0.0019)
(0.0070)
(0.0032)
(0.0032)
(0.0061)
(0.0199)
(0.0080)
(0.0124)
(0.0172)
6 of 17
Parameter a
Parameter b
61.9 (4.0)
95.3 (2.5)
95.9 (3.6)
108.2 (4.4)
118.8 (4.7)
122.6 (3.9)
123.7 (3.9)
145.2 (4.5)
156.1 (3.4)
155.4 (3.5)
157.6 (3.9)
157.1 (2.8)
155.9 (3.1)
169.4 (4.6)
191.4 (4.8)
138.2 (3.5)
636.1
635.9
639.4
638.8
639.0
638.7
637.2
635.3
636.5
638.5
639.4
638.6
635.8
639.8
635.9
637.2
(15.7)
(15.5)
(16.1)
(15.9)
(15.6)
(15.9)
(16.7)
(16.1)
(15.9)
(16.2)
(16.1)
(16.0)
(15.4)
(15.2)
(16.0)
(13.5)
Parameter c
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
0.010
(0.00097)
(0.00092)
(0.00091)
(0.00094)
(0.00092)
(0.00097)
(0.00095)
(0.00095)
(0.00096)
(0.00093)
(0.00096)
(0.00093)
(0.00095)
(0.00096)
(0.00096)
(0.00095)
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
G01030
Figure 6. Sampling history for parameter a in the WC-model for Acer rubrum and its posterior probability density distribution for assumptions on (a) Prior1 and (b) Prior2.
n = 60,000 sampling using a t-test. (To justify the use of a
t-test, we tested null hypotheses that the PDFs were normally distributed using a Shapiro-Wilk test. At the 95%
confidence level, the test did not reject the null hypothesis
of normality.) The t-test revealed that the means of the
two distributions are similar (e.g., t = 0.5, p = 0.93),
suggesting reasonable convergence after 20,000 iterations.
[27] We then tested our model’s ability to predict budburst for the years 2002–2006 at Harvard Forest (these
years were not used in the model calibration). This is
illustrated in Figure 7a for three prevalent species at Harvard Forest: Acer rubrum, Quercus rubra, and Acer saccharum. In all cases, the bias is less than one day, and the
RMSE is less than the observational error (3 days). The
model also successfully captures interannual variations of
budburst date (Table 5). Model performance for other
species (not shown) is comparable.
[28] We performed additional evaluation of our budburst
model using 2000–2009 data from UWM [Schwartz and
Hanes, 2010b]. This was possible for four species (Quercus rubra, Betula papyrifera, Fraxinus americana, and
Cornus alternifolia) for which budburst data is available at
both UWM and Harvard Forest. The model performs particularly well for Quercus rubra (Figure 7b, Table 5), giving
a bias of less than one day and an RMSE is similar to the
observational error. For Betula papyrifera and Fraxinus
americana, the model is highly correlated with the observations (Table 5), indicating that the model can successfully
capture the interannual variability. However, the model
exhibits systematic biases of 4 to 6 days. In contrast, in
Figure 7. Evaluation of species-specific model against (a) 2002–2006 budburst data at Harvard Forest
and (b) 2000–2009 budburst data at UW–Milwaukee.
7 of 17
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
G01030
G01030
Table 5. Evaluation of the Budburst Model at Harvard Forest and UW-Milwaukee
Harvard Forest (2002–2006)
Species
Red oak
Sugar maple
Red maple
-
Cor.
0.82
0.91
0.78
-
Bias
0.85
0.41
0.85
-
UW–Milwaukee (2000–2009)
RMSE
2.8
2.0
2.3
-
Species
Red oak
Paper birch
White-ash
Alt-leaf dogwood
the case of Cornus alternifolia, the bias is small (2 days),
but the model’s correlation with observations is weakest of
all the species considered here.
[29] A novel feature of RJMCMC is its ability to quantify
the probabilities associated with the different models. Our
optimizations show stronger support for a WC-budburst
model than for a W-budburst model for 15 species (Acer
pensylvanicum, Acer saccharum, Amelanchier canadensis,
Prunus serotina, and Quercus alba, Acer rubrum, Betula
alleghaniensis, Betula lenta, Betula papyrifera, Cornus
alternifolia, Crategus sp., Fagus grandefolia, Fraxinus
americana, Populus tremuloides, and Quercus rubra). For
many of these species, support for the WC-budburst model is
decisive (Table 2). For the other 2 species (Hamamelis virginiana and Quercus velutina) the simpler W-budburst
model is to be preferred, but the margin of preference is relatively small (Table 2). It is possible that a slightly longer
observation record would ultimately lead to the WC-budburst
model being preferred.
Cor.
0.74
0.82
0.95
0.35
Bias
0.3
4.0
6.2
2.3
RMSE
2.5
4.6
6.5
4.0
(“Expt 5”), (6) a chilling model simulation using the parameters in ORCHIDEE (“Expt 6”).
[31] The rationale behind this set of experiments is as
follows: comparison between CTR and Expt 1 indicates the
uncertainty in the carbon budget related to parameter
uncertainties, comparisons between CTR and Expt 2 indicate the uncertainty in the carbon budget related to hypotheses selection, comparison between CTR and Expt 3 and
Expt 4 indicates the uncertainty in the carbon budget related
to species selection, and comparisons between CTR and
Expt 5 and Expt 6 indicates differences between our phenology models and the phenology models in other DGVMs
(e.g., CLM-DGVM and ORCHIDEE).
4.2. Sensitivity of Terrestrial Carbon Budgets
to Budburst
[30] To understand the uncertainties in terrestrial carbon
budgets that are related to budburst uncertainty, we performed seven 500-year LM3 simulations (Table 6). All
simulations were forced with the “quasi-realistic” atmospheric forcing used by Sheffield et al. [2006]. This forcing
data set spans 1948–2008. Throughout the 500-year simulation, the forcing from 1948 to 2008 was recycled. At the
end of 300 years, soil carbon and vegetation carbon pools
were completely spun-up. We analyzed the final 20 years
corresponding to 1989–2008 climate. Our control simulation
consisted of a WC-model simulation using the parameters
(see Table 6) of Acer rubrum (hereafter denoted “CTR”).
This was complemented by: (1) a chilling model simulation
using the optimal parameters minus one standard deviation of
Acer rubrum (“Expt 1”), (2) a warming model using optimal
parameters of Acer rubrum (“Expt 2”), (3) a chilling model
using optimal parameters of Populus tremuloides (“Expt 3”),
(4) a chilling model using optimal parameters of averaged
budburst dates over 17 species (“Expt 4”), (5) a warming
model simulation using the parameters in CLM-DGVM
Table 6. Summary of LM3 Simulations
Simulation
Parameter
CTR
Expt 1
Expt 2
Expt 3
Expt 4
Expt 5
Expt 6
a: 156.1 b: 636.5 c: 0.01
a: 152.7 b: 620.6 c: 0.01
a: 145.2
a: 95.9 b: 639.4 c: 0.01
a: 138.2 b: 637.9 c: 0.01
a: 100
a: –68 b: 638 c: 0.01
Figure 8. Simulated averaged seasonal course in daily
mean (a) leaf area index (LAI), (b) net ecosystem productivity (NEP) during 1989 to 2008 in 9 experiments, and (c) differences of simulated leaf onset date and zero-crossing date
between CTR and the other six experiments.
8 of 17
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
G01030
Table 7. Differences of Simulated Leaf Area Index (LAI), Gross Primary Productivity (GPP), Vegetation Respiration (VR), Soil Respiration (SR), and Net Ecosystem Productivity (NEP) Between Experiments
Season
Difference
LAI (m2/m2)
GPP (KgC/m2day)
VR (KgC/m2day)
SR (KgC/m2day)
NEP (KgC/m2day)
Spring (Apr-May)
Expt 3-CTR
Expt 5-CTR
Expt 6-CTR
Expt 3m-CTR
Expt 5m-CTR
Expt 3-CTR
Expt 5-CTR
Expt 6-CTR
Expt 3m-CTR
Expt 5m-CTR
0.26 (8.9%)
0.29 (9.9%)
0.57 (20%)
1.25 (42.9%)
1.27 (40.2%)
1.12 (16%)
1.09 (14%)
0.10 (1.4%)
0.21 (2.8%)
0.21 (2.8%)
1.47 (27.9%)
1.38 (26.4%)
0.93 (16%)
1.93 (37.8%)
1.80 (35.2%)
0.23 (1.8%)
0.19 (1.5%)
0.001(0.1%)
0.01 (0.1%)
0.01 (0.1%)
0.43 (18%)
0.42 (17.6%)
0.40 (18%)
0.85 (36.7%)
0.79 (34.2%)
0.62 (9.3%)
0.55 (8.2%)
0.05 (0.7%)
0.12 (1.5%)
0.11 (1.5%)
0.43 (11.9%)
0.41 (10.6%)
0.01(0.2%)
0.05 (1.3%)
0.06 (1.4%)
1.11 (20.8%)
1.03 (19.1%)
0.15 (2.8%)
0.32 (6.0%)
0.30 (5.8%)
0.62 (+79.8%)
0.57 (+73.6%)
0.51 (65%)
1.03 (132.7%)
0.95 (122.6%)
0.72 (86%)
0.67 (80%)
0.19 (29.9%)
0.41 (49%)
0.39 (46%)
Summer (Jun-Jul)
[32] We calculated the 20-year climatology of daily
mean leaf area index (LAI) for the different experiments
(Figure 8a). Differences in budburst dates among the
experiments indicate that the selection and parameterization
of budburst can induce a bias of up to two weeks. The earliest budburst dates are observed on day 110 in Expt 5 and
on day 114 in Expt 3; the latest budburst date is observed in
on day 128 in Expt 6. For comparison, budburst occurred on
day 123 of the CTR experiment (Figure 8c). This distinctive
early onset in Expt3 indicates that there is sensitivity to the
species used to parameterize the LM3 broadleaf deciduous
plant functional type. The relatively large differences in Expt
5 and Expt 6 are unsurprising, since these parameters were
not obtained by calibration to the Harvard Forest data.
[33] We note also that there is a sudden drop of LAI in Expt
3 and Expt 5 around day 122. In the current LM3 phenology,
leaf drop is triggered when monthly mean temperature falls
below 10°C. This drop is not realistic for Harvard Forest
vegetation, and so these simulations underscore the point that
different aspects of model phenology are interrelated, and
ultimately must be parameterized in a self-consistent manner.
To prevent this springtime leaf drop, two additional simulations, Expt 3m and Expt 5m, were performed in which we
explicitly overrode the springtime leaf drop.
[34] The 20-year mean seasonal cycle of NEP also shows
differences among experiments (Figure 8b). To quantify
this, we define the NEP zero-crossing date as the day when
the 5-day running mean NEP exceeds 0—when the ecosystem switches from a carbon source to sink. The earliest zerocrossing dates occur in Expt 3 and Expt 5 (day 116), whereas
the latest zero-crossing date occurs in Expt 6 (day 132). The
differences between CTR and all the experiments are consistent with differences in leaf onset date (Figure 8c). This
consistency indicates that phenology parameterizations play
an important role in determining when the ecosystem
switches from a carbon source to a carbon sink.
[35] In the seasonal cycles of LAI and NEP, the largest
deviations from CTR occur in Expt 3, Expt 5, and Expt 6
(Figure 8). Differences in spring (April–May) and summer
(June–July) carbon budget variables between CTR and Expt
3, Expt 5, Expt 6, Expt 3m, and Expt 5m are summarized in
Table 7. In the spring, the simulations with relatively early
budburst (Expt 3 and Expt 5) have higher LAI than CTR by
up to 9.9%, but simulations with relatively late leaf onset
(e.g., Expt 6) have lower LAI than CTR by up to 20%.
Expt 3 and Expt 5 also have larger spring GPP and respiration than CTR, but GPP differences are larger than
respiration differences, and so earlier leaf onset leads to an
increase in NEP in spring. This increased NEP is more
clearly seen in Expt 3m and Expt 5m. Once the springtime
leaf drop in Expt 3 and Expt 5 is removed, earlier leaf
onset leads to an even larger increase in LAI in spring. In
contrast, Expt 6 has smaller NEP than CTR because it has
a smaller GPP than CTR. Although respiration was also
lower in Expt 6 than CTR, this was not enough to compensate for the drop in GPP.
[36] We also found that earlier leaf onset in spring influences summertime LAI and NEP dynamics. Summer LAI in
Expt 4 is 16% lower than LAI in CTR. However, the LAI in
Expt 3m is 2.8% larger than the LAI in CTR. Despite these
opposite changes in Expt 3 and Expt 3m LAI, Expt 3 and
Expt 3m NEP are both smaller than CTR NEP (by 86% and
49%, respectively). The lower NEP in Expt 3 relative to
CTR (difference of 0.72 g C m2 day1) is mainly
attributable to the related to decrease in LAI (difference
of 1.12 m2 m2) and increase soil respiration (difference of
+1.11 g C m2 day1) through enhanced decomposition of
soil organic matter related to leaf drop. Comparing Expt 3m
and CTR, it is enhanced respiration that causes Expt 3m NEP
to be less than CTR NEP. These results clearly indicate that
variations in spring leaf onset influence summertime as well
as springtime dynamics.
[37] Finally, we evaluated the sizes of the terrestrial
carbon pools in the last time step of each experiment
(Table 8). In general, all experiments simulate more vegetation carbon than soil carbon. Among experiments, the
largest carbon pool size (28.5 kg C m2 yr1) is observed in
Expt 3m, which is larger than the pool size in the CTR simulation by 10.5%. In contrast, the smallest carbon pool size
(25.2 kg C m2 yr1) occurred in Expt 3. These results
Table 8. Sizes of Terrestrial Carbon Pools at the End of 500 Years
of Simulation
Experiment
Vegetation
Carbon (Kg C /m2)
Soil Carbon
(Kg C /m2)
Total Carbon
(Kg C /m2)
CTR
Expt 1
Expt 2
Expt 3
Expt 4
Expt 5
Expt 6
Expt 4m
Expt 5m
15.75
15.78
15.75
15.11
14.11
14.92
15.97
16.18
16.17
11.35
11.39
11.36
11.26
11.09
11.26
11.56
11.86
11.82
27.11
27.18
27.12
26.73
25.20
26.18
27.53
28.05
27.99
9 of 17
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
G01030
G01030
Figure 9. (a) Risks of occurrence of spring frost of 17 species and (b) parameter a in budburst model of
17 species.
suggest that model predictions of terrestrial carbon storage
are sensitive to the details of how spring phenology is
modeled.
5. Discussion
[38] We focused on the long-term budburst observations
of 17 species at Harvard Forest. Through RJMCMC simulations, we found that for 15 of 17 species, a budburst model
including a chill requirement model is more highly supported by observations than a model without a chill
requirement. The preference of a model including a chill
requirement is qualitatively consistent with previous two
studies [e.g., Chiang and Brown, 2007; Richardson and
O’Keefe, 2009] at Harvard Forest. Comparison of our
results with these previous studies indicates that there is
unanimous agreement that 11 of the 17 species are likely to
have a chill requirement. In particular, all studies agree that
the four dominant species at Harvard Forest (Acer rubrum,
Quercus rubra, Quercus alba, and Betula alleghaniensis;
see http://harvardforest.fas.harvard.edu/) are best described
by a model including a chill requirement. Our study yielded
the additional information that the posterior probability of
the CW-model is five to six times higher than the posterior
probability of the W-model.
[39] Although the spring phenology model in the present
study is based on the concept of growing degree days, our
CW-model captures some of the mechanisms of budburst. In
particular, for the CW-model, spring phenology is highly
dependent on temperature during both the endodormancy
phase (the period during which the plant remains dormant
due to internal factors) and the ecodormancy phase (the
period during which the plant remains dormant due to
external, environmental conditions) [Chuine, 2000;
Hänninen and Kramer, 2007]. Buds are able to grow only
after chilling requirements have been satisfied (e.g., sufficient chilling days in CW-model); they subsequently break
after heat requirements have been completed (e.g., enough
forcing days in CW-model). Therefore, warming temperatures have a negative impact on endodormancy and a positive impact on ecodormancy.
[40] Implicit in our model is the idea that temperature is
the dominant factor controlling budburst. This is consistent
with previous studies that have argued that temperature
affects the process of bud development [Chuine, 2000;
Hänninen and Kramer, 2007] and is consistent with results
from growth chamber experiments [Mölmann et al., 2005].
However, other factors, including photoperiod, may also
have some influence on the budburst date [Campoy et al.,
2011]. This should be a second-order effect, as we are not
aware of any studies that demonstrate that photoperiod is
more dominant than temperature when predicting budburst.
This holds even for species such as beech, which are known
to be particularly sensitive to photoperiod [Vitasse et al.,
2009]. This work joins other recent studies [Morin et al.,
2009; Tanino et al., 2010] that demonstrate that even in
trees thought to be photoperiod controlled, temperature can
modify the timing of key phenological events. This is indeed
an issue that will require further study, and would greatly
benefit from long-term, species-specific budburst records at
other sites. Through the USA National Phenology Network,
the availability of such data sets may become a realistic
possibility over the next few years.
[41] A key question is whether the parameter values
obtained in our optimizations reflect actual differences of
budburst strategy between species. Although many factors
probably influence a species phenology (e.g., genetic
diversity, adaptation, evolution history, stem anatomy, and
shade tolerance [see Lechowicz, 1984]), one simple and
useful approach has been to view the adaption of the budburst of temperate trees to prevailing climatic conditions as a
result of a stabilizing selection caused by two opposite
driving forces of natural selection [Leinonen and Hänninen,
2002]. These include (i) survival adaptation, which is the
avoidance of spring frost damage after budburst, and (ii)
capacity adaptation, which is the effective use of growing
resources of the growing season through early budburst
[Hänninen and Hari, 1996]. The relationship between spring
frost risk and budburst date (Figure 9a) illustrates the interplay between survival and capacity adaptations. Spring frost
risk is estimated by recording the daily minimum temperatures (e.g., below 2°C) during the frost-sensitive period,
10 of 17
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
which was assumed to begin at the time of bud burst and end
when an additional 100 GDD have accumulated after bud
burst [Hannerz, 1994]. The spring frost risk of each species
was defined as proportion of years when temperatures below
2°C occurred during the frost-sensitive period out of the total
number of years involved in the calculations [Leinonen and
Hänninen, 2002].
[42] Overall, decreases of spring frost risk are correlated
with later budburst dates, indicating a tradeoff between
capacity adaptation and survival adaptation. A species with
early budburst (e.g., Populus tremuloides) strongly exhibits
capacity adaptation, and a species with later budburst (e.g.,
Acer rubrum) strongly exhibits survival adaptation. Our
species-specific parameter a reflects this tradeoff (Figure 9b).
These species-dependent features have strong implications
for ecosystem functioning (Figure 8). While earlier budburst
can lead to increased carbon uptake if environmental conditions are right, it can also lead to frost damage [Gu et al.,
2008].
[43] Identification of the prior information and observation
errors impact hypothesis evaluation in RJMCMC. Comparing the results between RJMCMC analyses using uniform
and Gaussian priors, we find that the selection of the optimal
model for each species was not influenced by prior information, but that the prior information did influence the
posterior uncertainties of optimal parameters. The sensitivity
of posterior probabilities to observational errors can also
influence hypothesis selection. With increases in observational errors, the posterior PDFs flatten out, indicating that it
is difficult to select a model when observations are of poor
quality. In contrast, with decreases in observational errors,
the posterior probability of complex models structure tends
to increase. This is intuitive; that parameterization of complex models for budburst prediction should require a sufficient number of high-quality observations. These results
also suggest the difficulty in parameterizing budburst
models with satellite-retrieved leaf onset dates. For example, MODIS and GIMMS LAI (or NDVI) data, which are
the most widely used in phenology studies, have 8-day and
15-day temporal resolution, respectively. At this level of
uncertainty, it becomes difficult to identify variations in
budburst due to a chilling requirement. In addition, some
previous studies suggested more complex budburst models
(e.g., a 6-parameter chill requirement model) [Hänninen
and Kramer, 2007] than the 1–3 parameter models considered here. However, our results indicate that construction
of complex models will likely require additional observations or reduced observational errors.
[44] We identified different optimal parameter values for
different species at Harvard Forest, indicating a differential
response to climate variability. This is consistent with results
in the previous studies [Fisher et al., 2006; Morin et al.,
2009; Richardson and O’Keefe, 2009] which suggested
that the phenological responses to climate change critically
depends on species composition. However, we note here that
intraspecies variations may be nearly as important (compare
Figures 1 and 2). For example, the STD between 17 species
in one sample year (e.g., 1992) is 6 days and the STD
between 5 individuals of Acer rubrum is 4 days. Similar
results hold in other years. Furthermore, the highest (and
lowest) budburst STD of a set of Acer rubrum individuals
occurs in the same year as the highest (and lowest) budburst
G01030
interspecies STD. Additional observations are should be
carried out to better characterize intraspecies variations in
budburst.
[45] Evaluation of our species-specific budburst models
against the UWM data set provides insights as to whether a
locally developed budburst model can be applied regionally
(Figure 7, Table 5). Some species (e.g., Quercus rubra) are
well-simulated at both the Harvard and UWM sites, while
other species may exhibit biases or differences in interannual
variability. This is not totally unexpected; to a certain extent,
the relationships between phenology and environmental
conditions may vary with location because of genetic variation [Lechowicz, 1984]. Additionally, the genetic distribution and responses of individual trees at specific locations
are controlled by shorter-term processes related to their
unique biogeographic histories, and these may be difficult to
predict. Further progress would be greatly aided by regional
and continental scale phenology data sets. One approach
would be to use remote sensing observations. Several remote
sensing studies tried to construct a large-scale phenology
model by using satellite-retrieved vegetation index [Botta
et al., 2000; Jolly et al., 2005; Stöckli et al., 2011].
While such models can capture the large-scale features of
phenology, a drawback to this approach is that it cannot
distinguish the species distributions on the ground [Fisher
et al., 2006]. To overcome this problem, it may be possible to complement remote sensing information with new
ground-based data sets (e.g., USA National Phenology
Network). Evaluating the phenology model developed here
against such nationwide data sets can help to improve our
understanding of phenology and will be the subject of
follow-up studies.
[46] We evaluated the influence of uncertainty in spring
phenology on the terrestrial carbon budget by incorporating
different spring phenology models into the LM3 terrestrial
biosphere model. We found that large differences in leaf
onset dates led to differences in NEP zero-crossing date (i.e.,
the date when the ecosystem switches from a carbon source
to a carbon sink). Also, we found that uncertainties in leaf
onset dates modulate seasonal mean carbon uptake. Simulations in which leaf onset was earlier than in CTR had
larger springtime NEP than CTR, and vice versa. This negative correlation between leaf onset dates and NEP occurs
because leaf onset date is negatively correlated with
springtime GPP (Table 7). Although respiration is also
negatively correlated with leaf onset date (Table 7), this is a
secondary effect. These simulated features are consistent
with observational results in deciduous forest [Piao et al.,
2007; Richardson et al., 2009]. Thus, our model simulations support the conclusion of earlier studies that earlier leaf
onset date leads to increased spring carbon uptake in temperate deciduous forests.
[47] We also found that spring phenology affects the
summertime carbon budget. We identified two mechanisms
by which earlier leaf onset leads to reduced summer NEP.
The first arises due to the leaf drop in spring in Expt 3 and
Expt 5. Although a spring leaf drop has not been a realistic
feature at Harvard Forest for at least the past few decades,
these simulations are nevertheless instructive. For example,
Gu et al. [2008] showed that foliage at other temperate forests can be damaged by cold weather, and that this can
inhibit summer canopy development. This simulation gives
11 of 17
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
a sense of what the impacts of such chill damage may
include. Furthermore, leaf damage by insect disturbance
may also lead to an LAI profile similar to that simulated here
[Schäfer et al., 2010]. A second mechanism affecting Expt
3, Expt 3m, Expt 5, and Expt 5m connects earlier leaf onset
to enhanced summertime respiration. This occurs because
these simulations have more soil carbon than the CTR simulation. A consequence is decreased summertime NEP.
[48] Summing up, we identified uncertainties in terrestrial
carbon budgets related to spring phenology in LM3 simulations that can be attributed to budburst model structure and
parameter values, and the LM3′s representation of plant
functional diversity. In the present study, the large differences between CTR and Expt3 are attributed to the choice of
whether to parameterize the model’s PFT with parameters
from Acer rubrum or from Populus tremuloides. This result
has important implications for improving the current performance of DGVMs. In particular, DGVMs can likely be
improved by increasing the number of plant functional types
(PFTs) that they simulate. More than one deciduous tree
type is likely to be necessary. Medvigy and Moorcroft
[2012] also emphasized that a small number of simulated
PFTs is likely to be a large source of bias for simulations of
northeastern U.S. forests.
[49] Recently, Richardson et al. [2012] compared the
representations of phenology in different ecosystem models
using flux tower data. They found large differences of phenology between models, and suggested that differences in
spring phenology led to differences in the simulated carbon
fluxes. Our paper takes a different approach. Here, we use
one model (LM3), but investigate carbon cycle uncertainty
coming from several different sources. The LM3 model is a
newly developed terrestrial ecosystem model and is part of
the Earth system model at the Geophysical Fluid Dynamics
Laboratory (GFDL). To date, only one paper using LM3 has
been published [Shevliakova et al., 2009]. Because LM3 is a
newly developed model, it has not yet been included in
model intercomparison studies. As LM3 is now the main
land model being used at the GFDL, we anticipate that it will
be included in future intercomparison studies.
[50] Finally, we found large uncertainties related to differences in spring phenology among DGVMs (Expt 5 and
Expt 6). Two recent climate-carbon cycle model intercomparison studies [Friedlingstein et al., 2006; Sitch et al., 2008]
showed some large differences in terrestrial carbon uptake
between models. They suggested that differences in simulated terrestrial carbon budgets are attributable to the different parameter combinations governing vegetation dynamics
in the models. Here, our results suggest phenology can be
considered as an important source of uncertainty between
DGVMs. Thus, more effort is needed to develop generalize
process-based phenology appropriate for an earth system
model. Extended local budburst or leafing observations with
several species as well as appropriate large-scale data sets are
required to constrain the process-based phenology models.
Appendix A: Overview of Monte Carlo Methods
A1. Estimation of Parameters with Markov Chain
Monte Carlo
G01030
probability density function (PDF) of x is then denoted P(x).
Let y denote a vector of observations. Then, the posterior
probability density function (PDF) of x given y is denoted
P(x|y). MCMC is a method for sampling P(x|y). After the
PDF has been approximated with MCMC, it is straightforward to estimate whatever statistic is desired, including
maximum likelihood estimates and uncertainty estimates. To
illustrate how the MCMC works, assume that the Markov
chain is currently at xi ∈ S. The procedure for generating
xi+1 ∈ S is as follows:
(1) Propose a new parameter set, xp ∈ S.
(2) Compute an acceptance probability, a.
(3) Draw a random number from the uniform distribution U(0,1).
(4) If the random number is less than a, then set xi+1 =
xp. Otherwise, set xi+1 = xi.
[52] The generation of the proposal xp is allowed to
depend on xi but not on other elements of the Markov chain.
One typically proceeds by defining a proposal distribution,
q(xi,xp), that gives the probability of proposing a move
from xi to xp. The only requirement on q is that it be
ergodic; i.e., the MCMC must be able to move from one
point in S to any other point in S in a finite number of steps.
The computational efficiency of the MCMC is strongly
influenced by the choice of q [Green and Mira, 2001; Haario
et al., 2005; Guan et al., 2006]. For example, if xi happens
to be near the maximum of P(x|y), then it would typically
be efficient to reduce the probability of proposing an xp as
the distance between xp and xi increased. This would ensure
that the MCMC samples regions of S that have a relatively
large support. The functional form of q is often taken to be
a normal distribution with mean xi. This choice is always
ergodic and is computationally efficient for relatively simple
forms of P(x|y). However, if P(x|y) has many modes or is
otherwise pathological, other choices of q may lead to greater
efficiency [Guan et al., 2006].
[53] The acceptance probability a is given by the
Metropolis-Hastings rule [Metropolis et al., 1953; Hastings,
1970]:
!
P xp yÞ q xp ; xi
:
a ¼ min 1;
Pðxi j yÞ q xi ; xp
ðA1Þ
This choice of a ensures that the frequency that at which we
sample x will be converge to P(x| y), provided the number of
samples is sufficiently large. In evaluating equation (A1),
note that it is only necessary to calculate the posterior
probability up to a normalizing constant. To see this, we use
Bayes’s Theorem,
PðxjyÞ ¼
Pð yjxÞPðxÞ
;
Pð yÞ
ðA2Þ
where P(x) is the prior PDF and represents our knowledge of
x before the observations y are taken into account. In
equation (A2), P(y) will cancel out, and thus we do not need
to calculate it. P( y|x) is the likelihood. For the important
case of measurements with normally distributed errors and
a measurement error covariance matrix Smeas,
Pð yjxÞ ¼
[51] Consider a model M defined on a parameter space S.
Let x ∈ S denote a vector of parameters. The prior
12 of 17
1
ð2pÞNobs =2
1
1
exp ½ y M ðxÞT Smeas
½ y M ðxÞ :
jSmeas j
2
1
ðA3Þ
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
G01030
G01030
uinv(xi,ufor). The Jacobian of the transformation, |J|, is
given by:
∂ x ; u p inv jJ j ¼ :
∂ xi ; ufor Figure A1. Input data used in the regression example. Fifteen pairs of (x–y) variables with error bars. The lines show
the best fit constant, linear, quadratic, and cubic polynomials
(k = 1 to 4, respectively).
[56] While this formulation may seem cumbersome, it is
of great interest because it can easily be generalized to the
case where xi does not necessarily have the same dimension
as xp. In fact, xi and xp may correspond to totally different
parameters of two competing models. To illustrate this, let S1
be the parameter space associated with model 1 and let S2 be
the parameter space associated with model 2. Then, let xi ∈
S1, where xi is of dimension k1. Let xp ∈ S2, where xp is of
dimension k2. We start as before, drawing a vector ufor (this
time, with dimension k2) from the distribution gfor(ufor). The
mappings for the forward and inverse moves are again
described by equations (A4)–(A5). We again require that the
mapping between (xi,ufor) and (xp,uinv) be a diffeomorphism
so that we can solve for a unique uinv(xi,ufor). The acceptance
probability takes a form very similar to equation (A5); we
only require a slight change in notation:
$
%
P xp ; k2 yÞginv ðuinv Þ
jJ j :
a ¼ min 1;
Pðxi ; k1 jyÞgfor ufor
M(x) denotes the model’s predicted values for the observations, and Nobs is the number of observations. |Smeas|
denotes the determinant of Smeas.
A2.
Reversible Jump MCMC (RJMCMC)
[54] We first generalize our method of generating proposals for moving from xi ∈ S to xp ∈ S and afterward discuss
the case where xi and xp lie in different parameter spaces.
Accordingly, suppose that xi ∈ S and that xi has dimension k.
Instead of generating a new state xp ∈ S using q(xi,xp), we
make a slight change to our point of view. The first step of
the procedure is to generate a vector of k random numbers,
ufor, from a distribution gfor(ufor). We then define the forward mapping that depends on the current value of the chain
and the ufor:
xp ¼ hfor xi ; ufor
ðA4Þ
We can now imagine a hypothetical inverse mapping (hinv).
In this case, the starting point is xp, and we generate k random numbers uinv from a distribution ginv(uinv). These would
be used to generate xi:
xi ¼ hinv xp ; uinv
ðA5Þ
The only requirement on hfor and hinv is that the mapping
between (xi,ufor) and (xp,uinv) be a diffeomorphism [Green,
1995]. In this special case where xi and xp lie in the same
parameter space, hfor and hinv can represent the same mapping, and gfor and ginv can likewise represent the same
distribution.
[55] As described by Green [1995], the probability of
accepting such a proposal is given by:
$
%
P xp yÞginv ðuinv Þ
jJ j :
a ¼ min 1;
Pðxi jyÞgfor ufor
ðA6Þ
Note that the ufor need to be generated from gfor(ufor),
but that equations (A4)–(A5) can be solved for a unique
ðA7Þ
ðA8Þ
In equation (A8), the probability depends on the choice of
model, and it can be expanded in the usual way using
Bayes’s theorem; for example,
Pð yjxp ; k2 ÞP xp k2 ÞPðk2 Þ
P xp ; k2 yÞ ¼
:
Pð yÞ
ðA9Þ
Here, P(k2) is the prior probability of selecting model 2. The
posterior probability for model 2 is equated with the
fraction of samples in the Markov chain that corresponded
to model 2.
[57] As noted above, RJMCMC requires the computation
of the Jacobian of the parameter transformation. In many
cases, including those illustrated below, the Jacobian turns
out to be relatively simple [Sambridge et al., 2006;
Gallagher et al., 2009]. Perhaps the trickiest part of
RJMCMC is the development of efficient proposal functions
for the model-to-model jumps [Brooks et al., 2003]. However, computer code exists that automatically calculates
RJMCMC Jacobians and proposal functions, and it has
shown to be efficient for problems where the number of
unknowns is less than about 30 [Green, 2003; Malinverno
and Leaney, 2005].
A3.
RJMCMC: A Simple Example
[58] This example is based on section 3.3.1 of Sambridge
et al. [2006]. Consider N = 15 synthetically generated (x, y)
pairs of numbers and their associated error bars (Figure A1).
The x values were drawn from a uniform distribution
between 0 and 1. The y values satisfied: y = 0.6x + 0.3 + ɛ,
where ɛ is a draw from a Gaussian distribution with zero
mean and a standard deviation of s = 0.2. Suppose that we
did not a priori know that y(x) satisfied a simple linear
relationship. Instead, we expect the relationship to be some
polynomial, and our task is to determine which order
13 of 17
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
G01030
example, BIC = (30.5, 25.0, 27.4, 29.8) for k = (1, 2, 3, 4). As
might be hoped, the minimum BIC value indeed corresponds
to the linear model. However, BIC has an important limitation: it is a “point estimate,” evaluated only for a single best
fit parameter set. It does not provide any information on the
relative levels of support for different values of k.
[59] We can estimate the support for different values of k
using RJMCMC. As outlined in above section, two ingredients are necessary: a description of the prior, and an error
model for the measurements. Here, we assume uniform
priors,
p lj kÞ ¼
8
>
<
>
:
1
lU
lLj
j
lLj ≤ lj ≤ lU
j
0
otherwise
ð j ¼ 1; …; k Þ;
ðA12Þ
where (lLj , lU
j ) are the lower and upper values imposed for
lj. We allow a broad range of values, using lower limits of
(0, 2, 10, 30) and upper limits of (1.2, 2, 10, 30). We
express no prior preference on the model (i.e., the value
of k), other than that it be ≤4. This implies that the value
of the prior probability density function (PDF) for each
value of k is equal to 0.25 (Figure A2).
[60] Finally, we assume that the measurement errors are
Gaussian, and that the likelihood (L), which quantifies the
closeness of the model to the data (see above section), is
given by:
L¼
Figure A2. (a) The prior probability density for the number
of unknowns k in the regression model. The equal frequencies for k reflect the uniform prior imposed. (b) Same as
(a) but when the posterior probability density is sampled
using RJMCMC. Note the clear preference for two
unknowns with other values of k receiving much less
support.
of polynomial is appropriate. Obviously, a fifteenth-order
polynomial would exactly fit all the data points, but this
would likely constitute over-fitting. We consider here only
first-through-fourth-order polynomials. Figure A1 shows the
corresponding best fit curves. One approach to model selection is to consider the Bayesian Information Criterion (BIC)
[Schwarz, 1978], defined by:
BIC ¼ 2LL þ k logN ;
ðA10Þ
where LL is the log likelihood. Up to an additive constant, LL
is here given by
2
P
N
yi kj lj xi j1
1X
LL ¼ ;
2 i¼1
s2
ðA11Þ
and the unknowns are the li, (i = 1,…k). The first term
quantifies the match with the data, and the second term is a
penalty against having a large number of parameters. In our
1
ð2ps2 ÞN =2
6
!2 7
P
6
7
N
6 1X
7
yi kj lj xj1
i
5:
exp4
2 i¼1
s
ðA13Þ
[61] The RJMCMC algorithm outputs in a chain of samples, each consisting of a vector li, (i = 1,…k). The value of
k varies between samples. Figure 4b shows the posterior
PDF for the number of polynomial coefficients, k. This was
obtained by running the RJMCMC for 105 steps, collecting
every 10th sample and tabulating the frequency of k values.
The results of the RJMCMC indicate support in the ratio of
14%, 73%, 13%, and <1% for k = 1, 2, 3, 4, respectively.
These results favor selection of the linear model, but the
constant and quadratic models cannot be ruled out at the
95% confidence level. Additional data points or more
accurate observations would be necessary to more confidently rule out these hypotheses.
Appendix B: Implementation of RJMCMC
for the Phenology Problem
[62] We begin by illustrating the case of jumping from one
GDD + CD model to another GDD + CD model. This corresponds to a move within the same space S, and is therefore
a relatively simple case of RJMCMC. The location in statespace is defined by the three parameters a, b, c. Define
gfor(ufor) to be equal to a multivariate normal distribution
with mean 0 and covariance matrix equal to a 3 3 identity
matrix. Then, the forward transformation is defined as:
14 of 17
ap ¼ ai þ sa ufor;a
bp ¼ bi þ sb ufor;b :
cp ¼ ci þ sc ufor;c
ðB1Þ
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
As above, the subscript “i” denotes the current parameter
value and the subscript “p” denotes the proposed parameter
value. The characteristic size of the jump, determined by sa,
sb, and sc, must be determined by the researcher. Jumps that
are too large are inefficient because the MCMC will frequently explore regions of S with little support, while jumps
that are too small are also inefficient because many samples
are required to comprehensively sample the regions of S
with strong support. Generally, acceptance rates between 20
and 50% are indicative of efficient convergence of the
Markov chain to the posterior PDF [Roberts et al., 1997].
The hypothetical inverse transformation is given by:
ai ¼ ap þ sa uinv;a
bi ¼ bp þ sb uinv;b ;
ci ¼ cp þ sc uinv;c
uinv;a ¼ ufor;a
uinv;b ¼ ufor;b :
uinv;c ¼ ufor;c
ðB3Þ
Because gfor(ufor) = ginv(ufor) = ginv(ufor) = ginv(uinv),
ginv(uinv)/gfor(ufor) = 1. It is straightforward to show from
equations (B1) and (B3) that |J| = 1. The acceptance
probability of this move is therefore given by:
P xp yÞ
:
a ¼ min 1;
Pðxi jyÞ
"
GDD ¼ a þ b expðc90Þ exp c
day¼1
budburst
X
#!
CD 90
:
day¼1
ðB5Þ
This equation is exact. If the number of chill days is 90, then
the argument of the second exponential will be 0. In general,
at Harvard Forest, we would indeed expect the number of
chill days to be close to 90. We can now add and subtract a
term:
budburst
X
day¼1
GDD ¼ ½a þ b expðc90Þ
|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
baseline GDD threshold
"
"
þb expðc90Þ exp c
GDDthreshold ¼ ai þ bi expðci 90Þ þ saf ufor;a :
budburst
X
#!
CD 90
#
1 :
day¼1
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
correction due to chill day variability
ðB6Þ
Provided the number of chilling days is roughly 90,
GDDthreshold (equation (2)) should be in rough correspondence with the “baseline GDD threshold” (equation (B6))
ðB7Þ
For simplicity, we will henceforth take saf = sa, though this
restriction can easily be relaxed if proposals are not being
accepted at an adequate rate. As before, ufor,a is a draw from
a normal distribution of mean 0 and standard deviation 1.
[64] The inverse transformation relies on the priors to first
generate bi and ci:
bi ¼ uinv;b
ci ¼ uinv;c
:
ai ¼ GDDthreshold uinv;b exp uinv;c 90 þ sa uinv;a
ðB8Þ
uinv,b is a draw from the prior on b and uinv,c is a draw from
the prior on c. uinv,a is a draw from a normal distribution with
mean 0 and standard deviation 1. Then, ginv(uinv)/gfor(ufor) =
P(bi)P(ci). The Jacobian of this transformation is:
6
6
1
0
6
6
0
expð90ci Þ
6
J ¼4
90bi expð90ci Þ 0
saf
1
0
1
0
0
7
07
7
07
7:
15
0
ðB9Þ
Note that |J| = 1, so that the acceptance probability becomes:
a ¼ min 1;
ðB4Þ
[63] Equation (B4) also holds for a jump between two
GDD models. But what would be a sensible proposal for a
jump from a GDD + CD model to a GDD model? To illustrate the relationship between the two models, note that the
GDD + CD model can be written:
budburst
X
and the “correction due to chill day variability” (equation
(B6)) should be small. A computationally efficient rule for
transitioning between a GDD + CD model and a GDD
model may then be given by:
ðB2Þ
where the uinv would also be drawn from a multivariate
normal distribution with mean zero and covariance matrix
equal to the 3 3 identity matrix. We can solve for the uinv:
G01030
Pðxp ; GDDj yÞ
Pðbi ÞPðci Þ :
Pðxi ; GDD þ CDj yÞ
ðB10Þ
The jump from a GDD model to a GDD + CD model can be
constructed in the same way, yielding:
Pðxp ; GDD þ CDj yÞ
1
:
a ¼ min 1;
Pðbi ÞPðci Þ
Pðxi ; GDDjyÞ
ðB11Þ
[65] Acknowledgments. The authors wish to thank R. J. Stouffer for
helpful comments and discussions. This research was supported by award
NA08OAR4320752 from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce. The statements, findings, conclusions, and recommendations are those of the authors and do not
necessarily reflect the views of the National Oceanic and Atmospheric
Administration or the U.S. Department of Commerce. The authors appreciate very helpful and constructive comments made by editors and reviewers.
We thank J. O’Keefe for making the Harvard Forest phenology data available (http://harvardforest.fas.harvard.edu/), and we thank M. D. Schwartz,
in collaboration with G. Meyer and J. Reinartz, for making the University
of Wisconsin–Milwaukee (UWM) field station phenology data available
(http://www4.uwm.edu/fieldstation/). We also thank the agencies and institutions that funded the long-term measurements at these sites.
References
Akaike, H. (1973), Information theory and an extension of the maximum
likelihood principle, in Proceedings of the 2nd International Symposium
on Information Theory, edited by B. N. Petrov and F. Csaki, pp. 267–281,
Akad. Kiado, Budapest.
Baldocchi, D. D., and S. Wong (2008), Accumulated winter chill is
decreasing in the fruit growing regions of California, Clim. Change,
87, 153–166, doi:10.1007/s10584-007-9367-8.
Baldocchi, D. D., et al. (2005), Predicting the onset of net carbon uptake by
deciduous forests with soil temperature and climate data: A synthesis of
FLUXNET data, Int. J. Biometeorol., 49, 377–387, doi:10.1007/
s00484-005-0256-4.
15 of 17
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
Bodin, T., M. Sambridge, and K. Gallagher (2009), A selfparameterising
partition model approach to tomographic inverse problems, Inverse
Probl., 25, 055009, doi:10.1088/0266-5611/25/5/055009.
Bonan, G. B. (2008), Forest and climate change: Forcings, feedbacks, and
the climate benefits of forests, Science, 320, 1444–1449, doi:10.1126/
science.1155121.
Botta, A., et al. (2000), A prognostic scheme of leaf onset using satellite
data, Global Change Biol., 6, 709–725, doi:10.1046/j.1365-2486.2000.
00362.x.
Brooks, S. P., P. Giudici, and G. O. Roberts (2003), Efficient construction
of reversible jump Markov chain Monte Carlo proposal distributions
(with discussion), J. R. Stat. Soc. B, 65, 3–39, doi:10.1111/14679868.03711.
Campoy, J. A., D. Ruiz, and J. Egea (2011), Dormancy in temperate fruit
trees in a global warming context: A review, Sci. Hortic. (Amsterdam),
130, 357–372, doi:10.1016/j.scienta.2011.07.011.
Cannell, M. G. R., and R. I. Smith (1983), Thermal time, chill days and prediction of budburst in picea sitchensis, J. Appl. Ecol., 20, 951–963,
doi:10.2307/2403139.
Chiang, J. M., and K. J. Brown (2007), Improving the budburst phenology
subroutine in the forest carbon model PnET, Ecol. Modell., 205(3–4),
515–526, doi:10.1016/j.ecolmodel.2007.03.013.
Chuine, I. (2000), A unified model for budburst of trees, J. Theor. Biol.,
207, 337–347, doi:10.1006/jtbi.2000.2178.
Chuine, I., and P. Cour (1999), Climatic determinants of budburst seasonality in four temperate-zone tree species, New Phytol., 143, 339–349,
doi:10.1046/j.1469-8137.1999.00445.x.
Fisher, J. I., J. F. Mustard, and M. A. Vadeboncoeur (2006), Green leaf phenology at Landsat resolution: Scaling from the filed to the satellite,
Remote Sens. Environ., 100, 265–279, doi:10.1016/j.rse.2005.10.022.
Fisher, J. I., A. D. Richardson, and J. F. Mustard (2007), Phenology model
from surface meteorology does not capture satellite-based greenup
estimations, Global Change Biol., 13, 707–721, doi:10.1111/j.13652486.2006.01311.x.
Foley, J. A., I. C. Prentice, N. Ramankutty, S. Levis, D. Pollard, S. Sitch,
and A. Haxeltine (1996), An integrated biosphere model of land surface
processes, terrestrial carbon balance, and vegetation dynamics, Global
Biogeochem. Cycles, 10(4), 603–628, doi:10.1029/96GB02692.
Fox, A., et al. (2009), The REFLEX project: Comparing different algorithms and implementations for the inversion of a terrestrial ecosystem
model against eddy covariance data, Agric. For. Meteorol., 149, 1597–
1615, doi:10.1016/j.agrformet.2009.05.002.
Friedlingstein, P., et al. (2006), Climate-carbon cycle feedback analysis, results
from the C4MIP model intercomparison, J. Clim., 19, 3337–3353,
doi:10.1175/JCLI3800.1.
Gallagher, K., et al. (2009), Markov chain Monte Carlo (MCMC) sampling
methods to determine optimal models, model resolution and model
choice for Earth science problems, Mar. Pet. Geol., 26, 525–535,
doi:10.1016/j.marpetgeo.2009.01.003.
Green, P. J. (1995), Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, 82, 711–732,
doi:10.1093/biomet/82.4.711.
Green, P. J. (2003), Trans-dimensional Markov chain Monte Carlo, in
Highly Structured Stochastic Systems, Oxford Stat. Sci. Ser., vol. 27,
edited by P. J. Green, N. L. Hjort, and S. Richardson, pp. 179–198,
Oxford Univ. Press, Oxford, U. K.
Green, P. J., and A. Mira (2001), Delayed rejection in reversible jump
Metropolis-Hastings, Biometrika, 88, 1035–1053.
Gu, L., P. J. Hanson, W. M. Post, D. P. Kaiser, B. Yang, R. Nemani, S. F.
Pallardy, and T. Meyers (2008), The 2007 eastern US spring freeze:
Increased cold damage in a warming world?, BioScience, 58, 253–262,
doi:10.1641/B580311.
Guan, Y., et al. (2006), Markov chain Monte Carlo in small worlds, Stat.
Comput., 16, 193–202, doi:10.1007/s11222-006-6966-6.
Haario, H., E. Saksman, and J. Tamminen (2005), Componentwise adaptation for high dimensional MCMC, Comput. Stat., 20, 265–273,
doi:10.1007/BF02789703.
Hannerz, M. (1994), Predicting the risk of frost occurrence after budburst of
Norway spruce in Sweden, Silva Fennica, 28, 243–249.
Hänninen, H., and P. Hari (1996), The implications of geographical variation
in climate for differentiation of bud dormancy ecotypes in Scots pine, in
Production Process of Scots Pine: Geographical Variation and Models,
Acta Forest. Fennica, vol. 254, edited by P. Hari, J. Ross, and M. Mecke,
pp. 11–21, Finn. Soc. of For. Sci, Helsinki.
Hänninen, H., and K. Kramer (2007), A framework for modelling the
annual cycle of trees in boreal and temperate regions, Silva Fennica,
41, 167–205.
Hastings, W. K. (1970), Monte Carlo sampling methods using Markov chain
and their applications, Biometrika, 57, 97–109, doi:10.1093/biomet/57.1.97.
G01030
Hopcroft, P. O., K. Gallagher, C. C. Pain, and F. Fang (2009), Threedimensional simulation and inversion of borehole temperatures for
reconstructing past climate in complex settings, J. Geophys. Res.,
114, F02019, doi:10.1029/2008JF001165.
Hunter, A. F., and M. J. Lechowicz (1992), Predicting the timing of budburst in temperate trees, J. Appl. Ecol., 29, 597–604, doi:10.2307/
2404467.
Jeong, S.-J., C.-H. Ho, and J.-H. Jeong (2009a), Increase in vegetation
greenness and decrease in springtime warming over east Asia, Geophys.
Res. Lett., 36, L02710, doi:10.1029/2008GL036583.
Jeong, S.-J., C.-H. Ho, K.-Y. Kim, and J.-H. Jeong (2009b), Reduction of
spring warming over East Asia associated with vegetation feedback, Geophys. Res. Lett., 36, L18705, doi:10.1029/2009GL039114.
Jeong, S.-J., C.-H. Ho, K.-Y. Kim, J. Kim, J.-H. Jeong, and T.-W. Park
(2010), Potential impact of vegetation feedback on European heat waves
in a 2 CO2 climate, Clim. Change, 99, 625–635, doi:10.1007/s10584010-9808-7.
Jeong, S.-J., C.-H. Ho, H.-J. Gim, and M. E. Brown (2011), Phenology
shifts at start vs. end of growing season in temperate vegetation over
the Northern Hemisphere for the period 1982–2008, Global Change
Biol., 17, 2385–2399, doi:10.1111/j.1365-2486.2011.02397.x.
Jolly, W. M., et al. (2005), A generalized, bioclimatic index to predict foliar
phenology in response to climate, Global Change Biol., 11, 619–632,
doi:10.1111/j.1365-2486.2005.00930.x.
Knorr, W., and J. Kattge (2005), Inversion of terrestrial ecosystem model
parameter values against eddy covariance measurements by Monte Carlo
sampling, Global Change Biol., 11, 1333–1351, doi:10.1111/j.13652486.2005.00977.x.
Krinner, G., et al. (2005), A dynamic global vegetation model for studies of
the coupled atmosphere-biosphere system, Global Biogeochem. Cycles,
19(1), GB1015, doi:10.1029/2003GB002199.
Lechowicz, M. J. (1984), Why do temperate deciduous trees leaf out at different times? Adaption and ecology of forest communities, Am. Nat., 124,
821–842, doi:10.1086/284319.
Leinonen, I., and H. Hänninen (2002), Adaptation of the timing of bud burst
of Norway spruce to temperate and boreal climates, Silva Fennica, 36,
695–701.
Levis, S., G. B. Bonan, M. Vertenstein, and K. W. Oleson (2004), The Community Land Model's Dynamic Global Vegetation Model (CLM-DGVM):
Technical description and user guide, NCAR Tech. Note 459+IA, 64 pp.,
Natl. Cent. Atmos. Res., Boulder, Colo.
Malinverno, A., and W. S. Leaney (2005), Monte carlo bayesian look-ahead
inversion of walkaway vertical seismic profiles, Geophys. Prospect., 53,
689–703, doi:10.1111/j.1365-2478.2005.00496.x.
Medvigy, D., and P. R. Moorcroft (2012), Predicting ecosystem dynamics at regional scales: An evaluation of a terrestrial biosphere model
for the forests of northeastern North America, Philos. Trans. R. Soc.
B, 367(1586), 222–235, doi:10.1098/rstb.2011.0253.
Medvigy, D., S. C. Wofsy, J. W. Munger, D. Y. Hollinger, and P. R.
Moorcroft (2009), Mechanistic scaling of ecosystem function and
dynamics in space and time: Ecosystem Demography model version
2, J. Geophys. Res., 114, G01002, doi:10.1029/2008JG000812.
Menzel, A., and P. Fabian (1999), Growing season extended in Europe
[abstract], Nature, 397, 659, doi:10.1038/17709.
Metropolis, N., A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller
(1953), Equation of state calculations by fast computing machines,
J. Chem. Phys., 21, 1087–1099, doi:10.1063/1.1699114.
Mölmann, J. A., et al. (2005), Low night temperature and inhibition of
giberellin biosynthesis override phytochrome action and induce bud set
and cold acclimation, but not dormancy in PHYA over expressors and
wild-type of hybrid aspen, Plant Cell Environ., 28, 1579–1588,
doi:10.1111/j.1365-3040.2005.01395.x.
Moorcroft, P. R., G. C. Hurtt, and S. W. Pacala (2001), A method for
scaling vegetation dynamics: The ecosystem demography model
(ED), Ecol. Monogr., 71, 557–586, doi:10.1890/0012-9615(2001)071
[0557:AMFSVD]2.0.CO;2.
Moore, D. J. P., J. Hu, W. J. Sacks, D. S. Schimel, and R. K. Monson
(2008), Estimating transpiration and the sensitivity of carbon uptake to
water availability in a subalpine forest using a simple ecosystem process
model informed by measured net CO2 and H2O fluxes, Agric. For.
Meteorol., 148, 1467–1477, doi:10.1016/j.agrformet.2008.04.013.
Morin, X., M. J. Lechowicz, C. Augspurger, J. O’Keefe, D. Viner, and
I. Chuine (2009), Leaf phenology in 22 North American tree species
during the 21st century, Global Change Biol., 15, 961–975, doi:10.1111/
j.1365-2486.2008.01735.x.
Murray, M. B., M. G. B. Cannell, and R. I. Smith (1989), Date of budburst
of fifteen tree species in birtian following climatic warming, J. Appl.
Ecol., 26, 693–700, doi:10.2307/2404093.
16 of 17
G01030
JEONG ET AL.: SPRING PHENOLOGY AND TERRESTRIAL CARBON
O’Keefe, J. (2000), Phenology of woody species, Harvard Forest Data
Archive: HF003, available at http://harvardforest.fas.harvard.edu:8080/
exist/xquery/data.xq?id=hf003, Harvard Univ., Cambridge, Mass.
Piao, S., P. Friedlingstein, P. Ciais, N. Viovy, and J. Demarty (2007),
Growing season extension and its impact on terrestrial carbon cycle in
the Northern Hemisphere over the past 2 decades, Global Biogeochem.
Cycles, 21, GB3018, doi:10.1029/2006GB002888.
Reichstein, M., et al. (2003), Inverse modeling of seasonal drought effects
on canopy CO2/H2O exchange in three Mediterranean ecosystems,
J. Geophys. Res., 108(D23), 4726, doi:10.1029/2003JD003430.
Richardson, A. D., and J. O’Keefe (2009), Phenological differences
between understory and overstory: A case study using the long-term
Harvard Forest records, in Phenology of Ecosystem Processes, edited
by A. Noormets, pp. 87–117, Springer, New York, doi:10.1007/9781-4419-0026-5_4.
Richardson, A. D., A. S. Bailey, E. G. Denny, C. W. Martin, and J. O’Keefe
(2006), Phenology of a northern hardwood forest canopy, Global Change
Biol., 12, 1174–1188, doi:10.1111/j.1365-2486.2006.01164.x.
Richardson, A. D., D. Y. Hollinger, D. B. Dail, J. T. Lee, J. W. Munger, and
J. O’Keefe (2009), Influence of spring phenology on seasonal and annual
carbon balance in two contrasting New England forests, Tree Physiol.,
29, 321–331, doi:10.1093/treephys/tpn040.
Richardson, A. D., et al. (2010a), Influence of spring and autumn phonological transitions on forest ecosystem productivity, Philos. Trans. R. Soc.
B., 365, 3227–3246, doi:10.1098/rstb.2010.0102.
Richardson, A. D., et al. (2010b), Estimating parameters of a forest ecosystem C model with measurements of stocks and fluxes as joint constraints,
Oecologia, 164, 25–40, doi:10.1007/s00442-010-1628-y.
Richardson, A. D., et al. (2012), Terrestrial biosphere models need better
representation of vegetation phenology: Results from the North American
Carbon Program Site Synthesis, Global Change Biol., 18, 566–584,
doi:10.1111/j.1365-2486.2011.02562.x.
Roberts, G. O., A. Gelman, and W. R. Gilks (1997), Weak convergence and
optimal scaling of random walk Metropolis algorithms, Ann. Appl. Probab., 7, 110–120, doi:10.1214/aoap/1034625254.
Sambridge, M., K. Gallagher, A. Jackson, and R. Pickwood (2006), Transdimensional inverse problems, model comparison and the evidence, Geophys. J. Int., 167, 528–542, doi:10.1111/j.1365-246X.2006.03155.x.
Sato, H., A. Itoh, and T. Kohyama (2007), SEIB-DGVM: A new dynamic
global vegetation model using a spatially explicit individual-based
approach, Ecol. Modell., 200(3–4), 279–307, doi:10.1016/j.ecolmodel.
2006.09.006.
Schäfer, K. V. R., K. L. Clark, N. Skowronski, and E. P. Hamerlynck
(2010), Impact of insect defoliation on forest carbon balance as assessed
with a canopy assimilation model, Global Change Biol., 16, 546–560,
doi:10.1111/j.1365-2486.2009.02037.x.
Schwartz, M. D. (1998), Green wave phenology, Nature, 394, 839–840,
doi:10.1038/29670.
Schwartz, M. D., and J. M. Hanes (2010a), Continental-scale phenology:
Warming and chilling, Int. J. Climatol., 30, 1595–1598, doi:10.1002/
joc.2014.
Schwartz, M. D., and J. M. Hanes (2010b), Intercomparing multiple measures of the onset of spring in eastern North America, Int. J. Climatol.,
30, 1614–1626, doi:10.1002/joc.2008.
G01030
Schwartz, M. D., R. Ahas, and A. Aasa (2006), Onset of spring starting earlier across the northern hemisphere, Global Change Biol., 12, 343–351,
doi:10.1111/j.1365-2486.2005.01097.x.
Schwarz, G. (1978), Estimating the dimension of a model, Ann. Stat., 6,
461–464, doi:10.1214/aos/1176344136.
Sheffield, J., G. Goteti, and E. F. Wood (2006), Development of a 50-yr
high-resolution global dataset of meteorological forcings for land surface
modeling, J. Clim., 19, 3088–3111, doi:10.1175/JCLI3790.1.
Shevliakova, E., S. W. Pacala, S. Malyshev, G. C. Hurtt, P. C. D. Milly, J. P.
Caspersen, L. T. Sentman, J. P. Fisk, C. Wirth, and C. Crevoisier (2009),
Carbon cycling under 300 years of land use change: Importance of the secondary vegetation sink, Global Biogeochem. Cycles, 23, GB2022,
doi:10.1029/2007GB003176.
Sitch, S., et al. (2008), Evaluation of terrestrial carbon cycle, future plant
geography, and climate-carbon cycle feedback using five Dynamic Global
Vegetation models (DGVMs), Global Change Biol., 14, 2015–2039,
doi:10.1111/j.1365-2486.2008.01626.x.
Stöckli, R., T. Rutishauser, I. Baker, M. A. Liniger, and A. S. Denning
(2011), A global reanalysis of vegetation phenology, J. Geophys. Res.,
116, G03020, doi:10.1029/2010JG001545.
Tanino, K. K., L. Kalcsits, S. Silim, E. Kendall, and G. R. Gray (2010),
Temperature-driven plasticity in growth cessation and dormancy development in deciduous woody plants: A working hypothesis suggesting
how molecular and cellular function is affected by temperature during
dormancy induction, Plant Mol. Biol., 73, 49–65, doi:10.1007/s11103010-9610-y.
Trudinger, C. M., et al. (2007), OptIC project: An intercomparison of optimization techniques for parameter estimation in terrestrial biogeochemical models, J. Geophys. Res., 112, G02027, doi:10.1029/2006JG000367.
Vitasse, Y., S. Delzon, E. Dufrene, J. Y. Pontailler, J. M. Louvet,
A. Kremer, and R. Michalet (2009), Leaf phenology sensitivity to temperature in European trees: Do within-species populations exhibit similar responses?, Agric. For. Meteorol., 149(5), 735–744, doi:10.1016/
j.agrformet.2008.10.019.
Wang, Y. P., D. D. Baldocchi, R. Leuning, E. Falge, and T. Vesala
(2007), Estimating parameters in a land-surface model by applying
nonlinear inversion to eddy covariance flux measurements from eight
FLUXNET sites, Global Change Biol., 13, 652–670, doi:10.1111/
j.1365-2486.2006.01225.x.
Zhang, X., D. Tarpley, and J. T. Sullivan (2007), Diverse responses of vegetation phenology to a warming climate, Geophys. Res. Lett., 34, L19405,
doi:10.1029/2007GL031447.
S.-J. Jeong and D. Medvigy, Atmospheric and Oceanic Sciences
Program, Department of Geosciences, Princeton University, 215 Sayre
Hall, 300 Forrestal Rd., Princeton, NJ 08544, USA. (sjeong@princeton.
edu; [email protected])
S. Malyshev and E. Shevliakova, Department of Ecology and
Evolutionary Biology, 106A Guyot Hall, Princeton University, Princeton,
NJ 08544, USA. ([email protected]; [email protected])
17 of 17