CPClimate of the PastCPClim. Past1814-9332Copernicus PublicationsGöttingen, Germany10.5194/cp-13-379-2017Development and evaluation of a system of proxy data assimilation
for paleoclimate reconstructionOkazakiAtsushiatsushi.okazaki@riken.jpYoshimuraKeiRIKEN Advanced Institute for Computational Science, Kobe, JapanInstitute of Industrial Science, The University of Tokyo, Tokyo, JapanAtsushi Okazaki (atsushi.okazaki@riken.jp)20April201713437939321November201622November201626February201728March2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://cp.copernicus.org/articles/13/379/2017/cp-13-379-2017.htmlThe full text article is available as a PDF file from https://cp.copernicus.org/articles/13/379/2017/cp-13-379-2017.pdf
Data assimilation (DA) has been successfully applied in the field of
paleoclimatology to reconstruct past climate. However, data reconstructed
from proxies have been assimilated, as opposed to the actual proxy values.
This prevented full utilization of the information recorded in the proxies.
This study examined the feasibility of proxy DA for paleoclimate
reconstruction. Isotopic proxies (δ18O in ice cores, corals, and
tree-ring cellulose) were assimilated into models: an isotope-enabled general
circulation model (GCM) and forward proxy models, using offline data
assimilation.
First, we examined the feasibility using an observation system simulation
experiment (OSSE). The analysis showed a significant improvement compared
with the first guess in the reproducibility of isotope ratios in the proxies,
as well as the temperature and precipitation fields, when only the isotopic
information was assimilated. The reconstruction skill for temperature and
precipitation was especially high at low latitudes. This is due to the fact
that isotopic proxies are strongly influenced by temperature and/or
precipitation at low latitudes, which, in turn, are modulated by the El
Niño–Southern Oscillation (ENSO) on interannual timescales.
Subsequently, the proxy DA was conducted with real proxy data. The
reconstruction skill was decreased compared to the OSSE. In particular, the
decrease was significant over the Indian Ocean, eastern Pacific, and the
Atlantic Ocean where the reproducibility of the proxy model was lower. By
changing the experimental design in a stepwise manner, the decreased skill
was suggested to be attributable to the misrepresentation of the atmospheric
and proxy models and/or the quality of the observations. Although there
remains a lot to improve proxy DA, the result adequately showed that proxy DA
is feasible enough to reconstruct past climate.
Introduction
Knowledge of past conditions is crucial for understanding long-term climate
variability. Historically, two approaches have been used to reconstruct
paleoclimate; one based on the empirical evidence contained in proxy data,
and the other based on simulation with physically based climate models.
Recently, an alternative approach combining proxy data and climate
simulations using a data assimilation (DA) technique has emerged. DA has long
been used for forecasting weather and is a well-established method. However,
the DA algorithms used for weather forecasts cannot be directly applied to
paleoclimate due to the different temporal resolution, spatial extent, and
type of information contained within observation data (Widmann et al., 2010).
The temporal resolution and spatial distribution of proxy data are
significantly lower (seasonal at best) and sparser than the present-day
observations used for weather forecasts, and the information we can get does
not measure the direct states of climate (e.g., temperature, wind, pressure), but represents proxies of those states (e.g., tree-ring width,
isotopic composition in ice sheets). Thus, DA applied to paleoclimate
is only loosely linked to the methods used in the more mature field of
weather forecasting, and it has been developed almost independently from
them.
Several DA methods have been proposed for paleoclimate reconstruction (von
Storch et al., 2000; van der Schrier et al., 2005; Dirren and Hakim, 2005;
Goosse et al., 2006; Bhend et al., 2012; Dubinkina and Goosse, 2013; Steiger
et al., 2014), and paleoclimate studies using DA have successfully determined
the mechanisms behind climate changes (Crespin et al., 2009; Goosse et al.,
2010, 2012; Mathiot et al., 2013). In previous studies, the variables used
for assimilation have been data reconstructed from proxies (e.g., surface air
temperature) because observation operators or forward models for proxies have
not been readily available. Hereafter, the DA method that assimilates
reconstructed data from proxies is referred to as reconstructed DA. Recently,
proxy modelers have developed and evaluated several forward models (e.g., Dee
et al., 2015, and references therein). Thanks to that, currently a few studies
have started attempting to assimilate proxy data directly (Acevedo et al.,
2016a, b; Dee et al., 2016).
The main advantage of proxy DA over reconstructed DA is the richness of
information used for assimilation. In previous studies, only a single
reconstructed field was assimilated. However, proxies are influenced by
multiple variables. Hence, the assimilation of a single variable does not
use the full information recorded in the proxies.
The reconstruction method itself also limits the amount of information. The
most commonly used climate reconstruction is an empirical and statistical
method that relies on the relationships between climate variables and
proxies observed in present-day observations. These relationships are then
applied to the past climate proxies to reconstruct climate prior to the
instrumental period. Most of the studies using this approach assume that the
relationship is linear. However, this assumption imposes considerable
limitations in which specific climate proxies can be used, and proxies that
do not satisfy the assumption have generally been omitted (e.g., PAGES 2k
Consortium, 2013). Because information on paleoclimate is scarce, it is
desirable to use as much information as possible.
Furthermore, the reconstruction method also limits the quality of information
provided. The method also assumes stationarity of the relationship between
the climate and the proxies. However, this assumption has been shown to be
invalid for some cases (e.g., Schmidt et al., 2007; LeGrande and Schmidt,
2009). In the case of reconstructed DA, the assimilation of such questionable
reconstructed data would provide unrealistic results. In the case of proxy
DA, however, the skill of the assimilation is expected to be unchanged,
provided the model can correctly simulate the non-stationarity.
The concept of proxy data assimilation is not new, and has been proposed in
previous studies (Hughes and Ammann, 2009; Evans et al., 2013; Yoshimura et
al., 2014; Dee et al., 2015). Yoshimura et al. (2014) demonstrated that the
assimilation of the stable water isotope ratios of vapor improves the
analysis for current weather forecasting. They performed an observation
system simulation experiment (OSSE) assuming that isotopic observations from
satellites were available every 6 h. Because the isotope ratio of water
is one of the most frequently used climate proxies, this represents a
significant first step toward improving the performance of proxy data
assimilation in terms of identifying suitable variables for assimilation.
However, it is not yet clear whether it is feasible to constrain climate only
using isotopic proxies whose temporal resolution and spatial coverage are
much longer and sparser than those of the specific study.
This study examined the feasibility of isotopic proxy DA for the
paleoclimate reconstruction on the interannual timescale. Because the study
represents one of the first attempts to assimilate isotopic variables on
this timescale, we adopted the framework of an OSSE, as in previous climate
data assimilations (Annan and Hargreaves, 2012; Bhend et al., 2012; Steiger
et al., 2014; Acevedo et al., 2016b; Dee et al., 2016). After the evaluation
of proxy DA in the idealized way, we conducted the study with “real” proxy
DA. We investigated which factors decreased or increased the skill of the
proxy DA. As a measure of skill, we report the correlation coefficient
throughout the paper.
In this study, we used only oxygen isotopes (18O) as proxies. The
isotope ratio is expressed in delta notation (δ18O) relative to
Vienna Standard Mean Ocean Water (VSMOW) throughout the paper. If the
original data were expressed in delta notation relative to Vienna Pee Dee
Belemnite (VPDB), they were converted to the VSMOW scale.
This paper is structured as follows. In the following section, the data
assimilation algorithm, models, data, and experimental design are presented.
Section 3 shows the results of the idealized experiment. Section 4 gives the
results of the real proxy DA. The discussion is presented in Sect. 5.
Finally, we present our conclusions in Sect. 6.
Materials and methodsData assimilation algorithm
We used a variant of the ensemble Kalman filter (EnKF; see Houtekamer and Zhang,
2016, and references therein): the sequential ensemble square root filter
(EnSRF; Whitaker and Hamill, 2002). EnSRF updates the ensemble mean and the
anomalies from the ensemble mean separately, and processes observations
serially one at a time if the observations have independent errors.
To assimilate time-averaged data, a slight modification was made for the method
following Bhend et al. (2012) and Steiger et al. (2014). In the modified
EnSRF, the analysis procedure is not cycled to the simulation (Bhend et al.,
2012); thus, the background ensembles can be constructed from existing
climate model simulations (Huntley and Hakim, 2010; Steiger et al., 2014). As
such, we can assimilate data with any temporal resolution coarser than the
model outputs. In this study, we focused on annual DA.
There are two ways to construct the background ensemble in the approach
mentioned above (hereafter offline DA): one using ensemble runs as in weather
forecasts (Bhend et al., 2012; Acevedo et al., 2016a, b) and the other using a
single run (Steiger et al., 2014; Dee et al., 2016). The latter uses the same
background ensemble for every analysis step. To reduce computational cost, we
chose the latter way, where the ensemble members are individual years. This
simplification was valid because the interannual variability in a single run
was inherently indistinguishable from the variability in the annual mean
within the ensemble of simulations in which the initial conditions were
perturbed, at least for atmospheric variables. Thus, the background ensembles
were the same for all the reconstruction years and did not contain any
year-specific boundary conditions and forcing information; hence, the
background error covariance was constant over time. Therefore, this study did
not consider non-stationarity between the proxies and climate. Despite the
limitations of the algorithm used in this study, it should be noted that the
proxy DA could address non-stationarity if one uses temporally varying
background ensemble. We return to this point in Sect. 5.
To control spurious long-distance correlations due to sampling errors, a
localization function proposed by Gaspari and Cohn (1999) with a scale of
12 000 km was used. The detailed procedure used for the algorithm is
described in Steiger et al. (2014).
Models
Isotope ratios recorded in ice cores, corals, and tree-ring cellulose were
assimilated. To assimilate these variables, forward models for the variables
are required. We used the forward model developed by Liu et al. (2013, 2014)
for corals, and that of Roden et al. (2000) for tree-ring cellulose. We assumed that
the isotopic composition of ice cores was the same as that of precipitation
at the time of deposition. Note that, in reality, the isotope ratio recorded
in ice cores is not always equal to that in precipitation due to
post-depositional processes (e.g., Schotterer et al., 2004). Because detailed
models that explicitly simulate the impact of all the processes involved in
determining the value of the ratio are not yet available, we used the isotope
ratio in precipitation for that in ice cores to avoid adding unnecessary
noise.
The isotopic composition in precipitation was simulated using an atmospheric
general circulation model (GCM) into which the isotopic composition of vapor,
cloud water, and cloud ice are incorporated as prognostic variables. The
model explicitly simulates the isotopic composition with all the details of
the fractionation processes combined with atmospheric dynamics and
thermodynamics, as well as hydrological cycles. Hence, the model simulates the
isotopic composition consistent with the modeled climate. Although many such
models have been developed previously (Joussaume et al., 1984, Jouzel et al.,
1987; Hoffmann et al., 1998; Noone and Simmonds, 2002; Schmidt et al., 2005;
Lee et al., 2007; Yoshimura et al., 2008; Risi et al., 2010; Werner et al.,
2011), we used a newly developed model (Okazaki and Yoshimura, 2017) based on
the atmospheric component of MIROC5 (Watanabe et al., 2010). The spatial
resolution was set to T42 (approximately 280 km) with 40 vertical layers.
The variability in δ18O recorded in coral skeleton aragonite
(δ18Ocoral) depends on the calcification temperature and
local δ18O in sea water (δ18Osw) at the time
of growth (Epstein and Mayeda, 1953). Previous studies have modeled
δ18Ocoral as the linear combination of sea surface
temperature (SST) and δ18Osw (e.g., Julliet-Leclerc and
Schmidt, 2001; Brown et al., 2006; Thompson et al., 2011), as follows:
δ18Ocoral=δ18Osw+aSST,
where a is a constant which represents the slope between δ18Ocoral and SST. In this study, the constant was uniformly set
to -0.22 ‰ ∘C-1 for all the corals, following
Thompson et al. (2011), and we used a model developed by Liu et al. (2013,
2014) to predict δ18Osw. The model is an isotopic mass
balance model that considers evaporation, precipitation, and mixing with
deeper ocean water. The coral model uses the monthly output of the
isotope-enabled GCM as its input, except for the isotope ratio of deeper
ocean water, which was obtained from observation-based gridded data compiled
by LeGrande and Schmidt (2006). After the model calculates the monthly
δ18Ocoral, it is arithmetically averaged to provide the
annual δ18Ocoral.
The isotope ratio in tree-ring cellulose (δ18Otree) was
calculated using a model developed by Roden et al. (2000). In this model,
δ18Otree is determined by the isotopic composition of the
source water used by trees for photosynthesis, and evaporative enrichment on
leaves via transpiration. In this study, the value of the isotopic
composition in the source water was arbitrarily assumed to be the moving
average, traced 3 months backward, of the isotopic composition in
precipitation at the site. Again, the model used the monthly output of the
isotope-enabled GCM as its input. After performing the tree-ring model
calculation, the monthly output was weighted using climatological net primary
production (NPP) to calculate the annual average. The NPP data were obtained
from the US National Aeronautics and Space Administration (NASA) Earth
Observation website (http://neo.sci.gsfc.nasa.gov).
Because the isotopic compositions of the proxies were simulated using the
output of the isotope-enabled GCM, their horizontal resolution was the same
as that of the GCM.
Experimental designControl experiment
The first experiment served as a control (CTRL) experiment, and used the
framework of an OSSE. In the experiment, the “simulation” and the “truth”
(nature run) were simulated by the same models, with the same forcing, but
with different initial conditions. Because the proxy models were driven by
the output of the GCM, the modeled proxies were consistent with the modeled
climate from the GCM. Thus, here we describe the experimental design for the
GCM. The GCM was driven by observed SST and sea-ice data (HadISST; Rayner et
al., 2003), and historical anthropogenic (carbon dioxide, methane, and ozone)
and natural (total solar irradiance) forcing factors. The simulation covered
the period of 1871–2007 (137 years).
Spatial distribution of proxies (δ18O in ice cores, corals, and
tree-ring cellulose, denoted by blue, pink, and green, respectively).
(a) Proxies spanning at least 1 year during 1871–2000 are mapped. (b) The
number of proxies is depicted as a function of time. (c–h) The spatial
distributions of the proxies are mapped for (c) 1871, (d) 1900, (e) 1930,
(f) 1960, (g) 1990, and (h) 2007.
Although the simulation period included recent times covered by
observational data, we assumed that the only variable that could be obtained
was the annual mean of δ18O in the proxies. We based this
assumption on the fact that we wished to perform the DA for a period in
which no direct measurements were available, and there were only climate
proxies covering the period. Therefore, the temporal resolutions of the
“observations” and “simulations” were also annual, considering the
typical temporal resolution of the proxies.
Observations were generated by adding Gaussian noise to the truth. The
spatial distribution of the observations mimicked that of the proxies. The
spatial distributions of each proxy for various periods are mapped in Fig. 1.
As can be seen from the figure, the distributions and the number of proxies
varied with time. However, for the sake of simplicity, the distributions of
the proxies were assumed to be constant over time in the CTRL experiment
(Fig. 1a). The size of the observation errors will be discussed in
Sect. 2.4.
The state vector consisted of five variables: surface air temperature and
amount of precipitation, as well as the isotopic composition in
precipitation, coral, and tree-ring cellulose. The first three variables
were obtained from the isotope-enabled GCM, and the other two variables were
obtained from the proxy models driven by the output of the GCM.
Real proxy data assimilation
The second (REAL) experiment assimilated proxy data sampled in the real
world. To mimic realistic conditions, SST and sea-ice concentration data to
be used as model forcing were modified from observational to modeled data. In
reality, there were no direct observations available for the target period of
the proxy DA. Therefore, to reliably evaluate the feasibility of proxy DA,
the first estimate should be constructed using modeled SST, as opposed to
observed SST. We used SST data from the historical run of the Coupled Model
Intercomparison Project Phase 5 (CMIP5; Taylor et al., 2007) from the
atmosphere–ocean coupled version of MIROC5 (Watanabe et al., 2010) obtained
from the CMIP5 data server (https://esgf-node.llnl.gov/search/cmip5/).
Because the experiment was not an OSSE, a nature run was not necessary.
Sensitivity experiments
Four sensitivity experiments were conducted to test the robustness of the
results of the proxy DA. In the first sensitivity experiment (CGCM), the
simulation run was constructed from the simulation forced by the modeled SST
and sea ice as in the REAL experiment. The other settings for the simulation
run were the same as those in the CTRL experiment. The nature run was the
same as that of the CTRL experiment. Thus, this experiment investigated how
the reconstruction skill of the results was decreased by using the simulated
SST compared to the CTRL.
In the second sensitivity experiment (VOBS), the experimental design was the
same as that in the CGCM, except for the number of proxies that were
assimilated. In the CGCM experiment, the distribution and number of proxies
were set to be constant over time, as in the CTRL experiment. In the VOBS
experiment, the distribution and number of proxies varied with time. Thus,
this experiment investigated how the reconstruction skill was decreased by
changing the number of proxies compared to the CGCM.
In the third sensitivity experiment (T2-Assim), reconstructed surface
temperature (Tr) was assimilated. The purpose of the experiment
was to compare the skill of the reconstructed DA with that of the proxy DA.
The experimental design was the same as that in the CTRL experiment, except
for the variables that were assimilated. The reconstructed temperature was
generated with a linear regression model of Tr=a+b×δ18O, where a and b are coefficients and δ18O is the
observed isotope ratio. The coefficients are calibrated with the observed
isotope ratio and the true temperature in the CTRL for the period of 1871 to
1950 (80 years). If the correlation between the isotope ratio and the
temperature during the calibration period was not statistically significant
(p<0.10), the data were discarded following Mann et al. (2008). This
screening process reduced the available data from 94 to 81 grid points.
The final sensitivity (M08) experiment was used to examine the sensitivity to
the observation network. The experimental design was the same as for the
CTRL, except for the spatial distribution of the proxy. The proxy network
used in the experiment was the same as that of Mann et al. (2008). We assumed
that isotopic information was available for all the sites, even when this was
not the case. For example, even if only tree-ring width data were available
at some of the sites in Mann et al. (2008), in this experiment we assumed
that isotopic data recorded in tree-ring cellulose were available at the
site. The number of grids containing observations were 94 and 250 for the
CTRL experiment and M08, respectively. The T2-Assim and the M08 were compared
with CTRL.
The experimental designs are summarized in Table 1.
Observation data
We used paleoclimate data archived at the National Oceanic and Atmospheric
Administration (NOAA;
https://www.ncdc.noaa.gov/data-access/paleoclimatology-data) and data
used in the PAGES 2k Consortium (2013). Additionally, 22 tree-ring cellulose
and 7 ice core data sets were collected separately from published papers. We
only used oxygen isotopic data (18O) whose temporal resolution was
higher than annual; proxies whose resolution was lower than annual were
excluded. The full list of proxies used in this study is given in the
Supplement. Following Crespin et al. (2009) and Goosse et al. (2010), all proxy
records were first normalized and then averaged onto a T42 grid box to
eliminate model bias and produce a regional grid box composite. To compare
the results from each experiment effectively, the assimilated variables were
all normalized in both the simulation and nature runs, as well as in the
observations in all the experiments.
Experimental designs. The observation network used in the CTRL
experiment is denoted as Orig.
SST data to driveSST data to driveAssimilated variableObservationMissingsimulation runtruth runnetworkdataCTRLHadISSTHadISSTSimulated δ18OOrigw/o missingCGCMModeled SSTHadISSTSimulated δ18OOrigw/o missingVOBSModeled SSTHadISSTSimulated δ18OOrigw/ missingREALModeled SST–Observed δ18OOrigw/ missingT2-AssimHadISSTHadISSTReconstructed T2 from simulated δ18OOrigw/o missingM08HadISSTHadISSTSimulated δ18OM08w/o missing
Annual mean δ18O in corals at a location where observational
data were available (1∘ N, 157∘ W) for (a) background
and (b) analysis. The black line indicates the truth, gray lines indicate
ensemble members, and green line indicates the ensemble mean.
Errors were added to the truth in a normalized manner to provide the
observation for all the experiment other than REAL. The normalized error was
uniformly set to 0.50 for all the proxies. This was based on the measurement
error of δ18O in ice cores being reported to range from 0.05 to
0.2 ‰ (e.g., Rhodes et al., 2012; Takeuchi et al., 2014), and the
corresponding normalized error (measurement error divided by standard
deviation of proxy) then ranges from 0.03 to 0.1, with an average of 0.06.
Similarly, the measurement error of δ18O in coral ranges from 0.03
to 0.11 ‰ (e.g., Asami et al., 2004; Goodkin et al., 2008), and the
corresponding normalized error ranges from 0.24 to 1.1, with an average of
0.53. The measurement error of δ18O in tree-ring cellulose ranges
from 0.1 to 0.3 ‰ (e.g., Managave et al., 2011; Young et al., 2015),
and the corresponding normalized error ranges from 0.08 to 0.55, with an
average of 0.28. In practice, due to the error of representativeness and that
in observation operator, it is common to increase the observation errors to
ensure that the analysis functions effectively (Yoshimura et al., 2014).
Furthermore, the measurement errors were not always available; therefore, a
uniform value of 0.5 was used for all the proxies. The corresponding
signal-to-noise ratio (SNR) is 2.0. The errors are assumed to be independent
for all the experiments.
Results from the OSSE
The time series of the first estimation, the analysis, and the truth
for δ18O in corals are compared as an example in Fig. 2 at a
location where observational data were available (1∘ N,
157∘ W). Because the first estimate was the same for all
reconstruction years, it is drawn as horizontal lines. After the
assimilation, the analysis agreed well with the truth (R=0.96, p<0.001). This confirmed that the assimilation performed well. We then
examined how accurately the other variables were reconstructed by
assimilating isotopic information. Figure 2 also shows the time series of
surface air temperature and precipitation for the same site. There was a
clear agreement between the analysis and the truth for both variables (R=0.92 and 0.88, respectively, for temperature and precipitation). This
indicated that temperature and precipitation were effectively reconstructed
by assimilating isotopic variables at this site. This was because the isotope
ratio in corals has a signature not only from temperature as given in
Eq. (1) but also precipitation (Liu et al., 2013); the correlation with
δ18Ocoral was -0.88 (p<0.001) for both temperature
and precipitation, respectively. This example shows that the isotopic proxy
records more than one variable.
Temporal correlation between the analysis and the truth. The green
dots represent the location of the proxy sampling site. The hatched areas
indicate where the correlation is not statistically significant (p>0.05).
Figure 3 maps the correlation coefficients between
the analysis and the truth for the isotope ratio, temperature, and
precipitation for 1970–1999. Because the first estimate was constant over
time, the temporal correlation between the first estimate and the truth
was zero everywhere. Thus, a positive correlation indicated that the DA
improved the simulation.
The correlation for δ18O in precipitation were high at the
observation sites, regardless of the proxy type. This was because δ18O in both corals and trees is affected by the isotopic composition in
precipitated water derived from sea water or soil water. The correlation for
δ18O in tree-ring cellulose were also high at the observation
sites. On the other hand, the high correlation for δ18O in corals
were not limited around the observation sites but were generally high at low
to midlatitudes. Similarly, the correlation was high at low to
midlatitudes for surface temperature. The correlation was also statistically
significant (p<0.05) around the observation sites in high latitude. In
contrast, closely correlated areas were restricted to low latitude for
precipitation.
First mode of EOF and the correlation between PC1 and temperature for (a, d) ice cores, (b, e) corals, and (c, f) tree-ring cellulose.
How can the spatial distribution of the correlation pattern be explained;
i.e., what do the proxies represent? To investigate this question, empirical
orthogonal function (EOF) analysis was conducted for the simulated δ18O in precipitation, corals, and tree-ring cellulose. Only grids that
contained observations were included in the analysis. The variables were
centered around their means before the analysis. The data covered the period
1871–2007. The EOF patterns and temporal correlations between surface
temperature and the characteristic evolution of EOF or the principal
components (PCs) of the first mode of each proxy are shown in Fig. 4.
The first mode of δ18O in ice core explains 14.3 % of the total
variance and it is the only significant mode according to North et al.'s (1982) rule of
thumb (the first and the second mode were indistinguishable).
The maximum loadings were in Greenland and Antarctica, where temperature
increase has been observed for the past hundred years (e.g., Hartmann et al.,
2013). Indeed, the PC1 shows the significant trend and is correlated with
global mean surface temperature (R=0.44, p<0.001). Therefore, it is
legitimate to regard ice core data as a proxy of global temperature as
revealed from observation (Schneider and Noone, 2007).
The first modes of δ18O in corals, and tree-ring cellulose
represent El Niño–Southern Oscillation (ENSO). The explained variance of the first modes of δ18O
in corals and tree-ring cellulose was 44.2 and 19.0 %, respectively.
The maximum loadings occurred in the central Pacific for corals, and Tibet
for tree-ring cellulose. The temporal correlation between the PC1s and NINO3
index was 0.95 and 0.37 for corals and tree-ring cellulose, respectively.
Because the isotopic composition in corals is influenced by sea temperature,
it is expected that the δ18O in corals from the central Pacific
records the ENSO signature. Interestingly, the analysis revealed that the
δ18O in tree-ring cellulose was also influenced by ENSO; hence,
this proxy contributes to the reconstruction of temperature and precipitation
over the tropical Pacific. Indeed, many previous studies have reported the
link between δ18O in tree-ring cellulose and ENSO (Sano et al.,
2012; Xu et al., 2011, 2013, 2015). Xu et al. (2011) inferred that the link is
caused by the association between ENSO and Indian monsoon rainfall (e.g.,
Rasmusson and Carpenter, 1983). The positive phase of ENSO results in a
decrease in summer monsoon rainfall in India, which leads to dry conditions
in summer. The decrease in precipitation leads to isotopically enriched
precipitation, and the dry conditions enhance the enrichment of water in
leaves. Correspondingly, the δ18O in tree-ring cellulose becomes
heavier than normal in the positive phase of ENSO. Due to the relationships
between the coral and tree-ring cellulose data and ENSO, the correlation
coefficient between the analysis and the truth for the NINO3 index was as
high as 0.95 (p<0.001).
Temporal correlation between the analysis and the truth for
(a–d) temperature and (e–h) precipitation, for each experiment. The green
dots
represent the location of the proxy sampling site. The hatched areas
indicate where the correlation is not statistically significant (p>0.05).
Although EOF analysis did not reveal any other significant correlation
between PCs and climate indices, climate indices for the North Atlantic
Oscillation and Southern Annular Mode calculated using the reconstructed
data were significantly correlated with the truth (0.59 and 0.46,
respectively).
Real proxy data assimilation
Based on the results of the idealized experiment described in the previous
section, we performed a “real” proxy DA, in which sampled and measured
data in the real world were assimilated.
The temporal correlation between the analysis and observations for
temperature and precipitation are shown in Fig. 5d and h. The observations were
obtained from HadCRUT3 (Brohan et al., 2006) for temperature, and
GHCN-Monthly Version 3 (Peterson and Vose, 1997) for precipitation.
Although the real proxy DA had reasonable skill, it was inferior relative to
the CTRL experiment. We investigated the cause of the decreased skill using
the outputs of the sensitivity experiments. The design of the experiments was
changed in a stepwise fashion to more realistic conditions of proxy data
assimilation from the idealized conditions. The correlations between the
analysis and the truth, or the observation, for the experiments are shown in
Fig. 5. The truths for the CGCM and VOBS experiments were the same as those
for the CTRL experiment. The global mean correlation coefficients for
temperature, precipitation, and NINO3 in the experiments are summarized in
Fig. 6. Note that the correlation was averaged in the same domain for all
the experiments to take into account the differences in representativeness.
Temporal correlation between the analysis and the truth for each experiment
for 1970–1999. The values for temperature and precipitation are the global
mean of the temporal correlations.
In the CGCM experiment, the temporal correlations between the analysis and
the truth were similar to those in the CTRL experiment for both temperature
and precipitation (Fig. 5b, f). This indicates that ENSO and its impacts were
well represented in the modeled SST used to construct the “simulation”.
Watanabe et al. (2010) reported similar modeled SST and observational values
for the amplitude of ENSO measured by the NINO3 index, and the spatial
patterns of the temperature and precipitation fields regressed on the NINO3
time series (see Figs. 13 and 14 in their report).
Because the number of proxies for assimilation differed from that in the
CGCM experiment, it was not straightforward to compare the results of the
REAL experiment with those of the CGCM experiment. To enable an effective
comparison of the results, the same number of proxies was assimilated in
the VOBS experiment as in the REAL experiment and the same settings were
used as in the CGCM experiment for the other variables. Consequently, the
performance of the assimilation of the VOBS experiment was similar to that
of the CGCM experiment for 1970–1999.
Temporal correlations between the analysis and the truth for (a, c) temperature and (b, d) precipitation, for (a, b) CTRL and (b, d) T2-Assim.
The green dots represent the location of the proxy sampling site. The
hatched areas mean that the correlation is not statistically significant
(p>0.05).
When the REAL and VOBS experiments were compared, the correlation
coefficients for temperature were significantly decreased over the Indian
Ocean, eastern Pacific, and Atlantic Ocean. These areas corresponded to areas
of low reproducibility in the coral model (Liu et al., 2014). The effects of
sea current and river flow in these areas, which were not included in the
coral model, were deemed to be considerable. Although we cannot attribute all
the decreased skill to the coral model, the reproducibility of δ18O
in corals in these areas requires improvement to enhance the performance of
the assimilation.
DiscussionComparison with the reconstructed temperature assimilation
Hughes and Ammann (2009) recommended assimilating measured proxy data, as
opposed to reconstructed data derived from the proxy data. This subsection
compares the results from the CTRL and T2-Assim experiments.
Signal-to-noise ratio (SNR) of the reconstructed temperature from the
observation used in CTRL.
Temporal correlations in North America between the analysis and the truth
for (a, b) temperature, and (c, d) precipitation, for experiments using
different proxy networks. The green dots represent the location of the proxy
sampling site. The hatched areas indicate where the correlation is not
statistically significant (p>0.05).
Figure 7 shows the spatial distribution of the correlation coefficients for
temperature and precipitation between the truth and the analysis for each
experiment. As a whole, the reconstruction skill was slightly degraded in
T2-Assim compared with CTRL with the global mean correlation coefficients for
temperature (precipitation) of 0.50 (0.30), 0.45 (0.23), for CTRL and
T2-Assim, respectively. On the other hand, the skill of proxy DA was not
always better than that of T2-Assim (e.g., temperature in tropical Atlantic
Ocean). Those pros and cons can be explained by the difference in the
observation error and the structure of Kalman gain. Figure 8 shows the SNR of
the Tr ranging from 0.22 to 1.6 with and average of 0.65.
Accordingly, the observation error is larger than that of CTRL everywhere,
and this resulted in the reduction of the reconstruction skill. On the other
hand, the better skill in T2-Assim should be owing to the difference in
Kalman gain. The Kalman gain determines analysis increments by spreading the
information in observations through the covariance between the prior and the
prior-estimated observations. We found that the correlations between the
prior (temperature) and the prior-estimated observation (temperature and
δ18O for T2-Assim and CTRL, respectively) were consistently higher
in T2-Assim than in CTRL (not shown) as Dee et al. (2016) showed. Thus, the
information in the observations was more effectively spread to the analysis
in T2-Assim, and this resulted in the improved skill. Note that the screening
process hardly hampered the reconstruction skill, because even if the
reconstructed temperature was fully used (i.e., not screened), the skill was
almost the same as T2-Assim.
Conducting similar experiments, Dee et al. (2016) also concluded that the
reconstruction skill was almost the same among proxy DA and reconstructed DA
if the relation between the reconstructed variable and the proxy is linear.
As isotope-enabled GCMs (Schmidt et al., 2007; LeGrande and Schmidt, 2009)
and observations and models for tree-ring width (D'Arrigo et al., 2008;
Evans et al., 2014; Dee et al., 2016) have demonstrated, however, the
relations between the proxies and climate are nonlinear and non-stationary
as well. Thus, it is difficult to expect that the skill of reconstructed DA
will be the same as that of proxy DA if we have the well-defined forward
proxy models (Hughes and Ammann, 2009). Although the current models are far
from perfect as implied in Sect. 4.2, the assimilation of proxy data will
offer a useful tool for the reconstruction of paleoclimate, in which the
relationship between the proxies and climate constructed with the present-day
conditions does not apply.
Sensitivity to the distribution of the proxies
The skill of the proxy DA was relatively low over Eurasia and North America,
even in the idealized experiment. It was unclear whether this was because of
limitations in the proxy data assimilation or the scant distribution of the
proxies. This subsection investigates the reasons for the relatively low
reproducibility in these areas by comparing the results of the CTRL and M08
experiments, focusing on North America. The number of grids for which proxy
data were available over North America was 11 and 126 for the CTRL and M08,
respectively.
The results for North America are shown in Fig. 9. The figure shows the
temporal correlation coefficients between the analysis and the truth for
surface air temperature and precipitation. The correlation coefficients were
calculated for 1970–1999. The skill was high in the area in which the
proxies were densely distributed for both variables. The values of the
coefficients averaged over the United States (30–50∘ N,
80–120∘ W) were 0.69 and 0.58 for temperature and precipitation,
respectively. Compared to the coefficients of 0.23 and 0.21, respectively, in
the CTRL experiment, the skill was enhanced for both variables. This implies
that the performance of the reconstruction was strongly dependent on the
distribution of the proxy data. Taking into consideration that proxy DA can
assimilate not only proxy data but also reconstructed data, proxy DA can take
advantage of the use of increasingly large amounts of data. Although it is
beyond the scope of this study, the combined use of these data is expected to
improve the performance of proxy DA.
Conclusion and summary
The feasibility of using proxy DA for paleoclimate reconstruction was
examined in both idealized and real condition experiments. The idealized
(CTRL) experiment had high skill at low latitudes due to the dependency of
coral data on temperature and precipitation in these regions, and the
correlation between ENSO and δ18O in corals in Pacific and
tree-ring cellulose in Tibet. Encouraged by the results, real proxy DA was
performed, where the simulation run was constructed from the simulation
forced by the modeled SST, and the real (observed) proxy data were
assimilated into the simulation (REAL experiment). The skill of the
reconstruction decreased compared to CTRL.
To investigate the reason for the relatively low skill in REAL compared to
CTRL, we performed additional experiments: CGCM and VOBS. The imperfect SST
used to drive the CGCM experiment resulted in a slight reduction of the
skill compared to the CTRL experiment with perfect SST. This was because
ENSO, which is the most important mode for the reconstruction, was well
represented in the modeled SST. The result is encouraging because to apply
the DA system to reconstruct ages where no instrumental observation is
available, we must rely on SST simulated by a coupled GCM. Similarly,
assimilating the unfixed number of the observation only slightly decreased
the reconstruction skill as shown in the comparison between CGCM and VOBS.
From the suite of experiments, more than half of the difference between CTRL
and REAL remained unexplained. This remaining difference can have a lot of
origins: e.g., errors in the isotope-incorporated atmospheric GCM, the proxy
models, and the proxy data. The errors in the models include
model biases and missing or overly simplified model components. For instance,
the coral model does not take into account the impact of ocean current or
river runoff in this study. Furthermore, post-depositional processes for
simulating isotope ratio in ice core were not included at all. Those
processes should be included to enable more efficient utilization of all the
data. The errors in proxy data include misrepresentation of the
targeted temporal and/or spatial scales. It is also possible that the data
were highly distorted by non-climatic factors. Thus, a thorough quality
control, similar to the procedures used in weather forecasting, should be
conducted before assimilation (e.g., Appendix B of Compo et al., 2011). At
this stage, it is difficult to show the relative contributions of each factor
to the degraded skill in REAL, it is necessary to estimate the impact of
structural errors in models as done in Dee et al. (2016).
Although the skill of proxy DA is dependent on the reproducibility of the
models and the number and quality of the observations, the results suggest
that it is feasible to constrain climate using only proxies. In particular,
ENSO and ENSO-related variations in temperature and precipitation should be
reliably reconstructed even with the current proxy DA system and proxy
network used in this study because the correlation coefficient between the
analysis and the observations was as high as 0.83 in the REAL experiment.
Although the reconstruction of ENSO is dependent on data from corals, and
the time span covered by corals is relatively short (a few hundred years),
ENSO can still be reliably reconstructed due to its global impact, as was
demonstrated in the relationship between isotopes in tree-ring cellulose
from Tibet.
Moreover, we expect that the reproducibility will increase as more proxy
data become available because it was heavily dependent on the spatial
distribution. Given that proxy DA can assimilate both proxy data and data
reconstructed from proxy, and that the reconstruction skill in reconstructed
DA is slightly superior to proxy DA, the combined use of the two types of data
is beneficial for the performance. In that case, care must be taken not to
assimilate dependent information (e.g., proxy data and reconstructed data
from the same proxy).
The DA algorithm used in this study did not consider non-stationarity among
proxies and climate variables because the Kalman gain was constant over
time. To address non-stationarity, the Kalman gain for a specific
reconstruction year should be constructed for several tens of years before
and after that year. Nevertheless, EnKF can only capture linear
relationships between observations and the modeled state. The use of other
algorithms, such as particle filter (e.g., van Leeuwen, 2009), or
four-dimensional variational assimilation (e.g., Rabier et al., 2000) should
be investigated in future studies for scenarios where nonlinearity is not
negligible. Thus, it is important in future studies to investigate
non-stationarity and nonlinearity among proxies and climate variables to
identify suitable algorithms for proxy DA.
Data for this paper are accessible through the Supplement.
The Supplement related to this article is available online at doi:10.5194/cp-13-379-2017-supplement.
The authors declare that they have no conflict of
interest.
Acknowledgements
The first author was supported by the Japan Society for the Promotion of
Science (JSPS) via a Grant-in-Aid for JSPS Fellows. This study was supported
by the Japan Society for the Promotion of Science (grants 15H01729, 26289160,
and 23226012), the SOUSEI Program, the ArCS project of MEXT, Project S-12 of
the Japanese Ministry of the Environment, and the CREST program of the Japan
Science and Technology Agency. Edited by: V.
Rath Reviewed by: two anonymous referees
References
Acevedo, W., Reich, S., and Cubasch, U., Towards the assimilation of
tree-ring-width records using ensemble Kalman filtering techniques, Clim.
Dynam., 46, 1909–1920, 2016a.Acevedo, W., Fallah, B., Reich, S., and Cubasch, U.: Assimilation of
Pseudo-Tree-Ring-Width observations into an Atmospheric General Circulation
Model, Clim. Past Discuss., 10.5194/cp-2016-92, in review,
2016b.Annan, J. D. and Hargreaves, J. C.: Identification of climatic state with
limited proxy data, Clim. Past, 8, 1141–1151, 10.5194/cp-8-1141-2012,
2012.
Asami, R., Yamada, T., Iryu, Y., Meyer, C. P., Quinn, T. M., and Paulay, G.:
Carbon and oxygen isotopic composition of a Guam coral and their
relationships to environmental variables in the western Pacific, Palaeogeogr.
Palaeocl., 212, 1–22, 2004.Bhend, J., Franke, J., Folini, D., Wild, M., and Brönnimann, S.: An
ensemble-based approach to climate reconstructions, Clim. Past, 8, 963–976,
10.5194/cp-8-963-2012, 2012.Brohan, P., Kennedy, J. J., Harris, I., Tett, S. F. B., and Jones, P. D.,
Uncertainty estimates in regional and global observed temperature changes: A
new data asset from 1850, J. Geophys. Res., 111, D12106, 10.1029/2005JD006548,
2006.Brown, J., Simmonds, I., and Noone, D.: Modeling δ18O in tropical
precipitation and the surface ocean for present-day climate, J. Geophys.
Res., 111, D05105, 10.1029/2004JD005611, 2006.
Compo, G. P., Whitaker, J. S., Sardeshmukh, P. D., Matsui, N., Allan, R. J.,
Yin, X., Gleason Jr., B. E, Vose, R. S., Rutledge, G., Bessemoulin, P.,
Brönnimann, S., Brunet, M., Crouthamel, R. I., Grnt, A. N., Groisman, P.
Y., Jones, P. D., Kruk, M. C., Kruger, A. C., Marshall, G. J., Maugeri, M.,
Mok, H. Y., Nordli, Ø., Ross, T. F., Trigo, R. M., Wang, X. L., Woodruff,
S. D., and Worley, S. J., The twentieth Century Reanalysis Project, Q. J.
Roy. Meteor. Soc., 137, 1–28, 2011.Crespin, E., Goosse, H., Fichefet, T., and Mann, M. E.: The 15th century
Arctic warming in coupled model simulations with data assimilation, Clim.
Past, 5, 389–401, 10.5194/cp-5-389-2009, 2009.
D'Arrigo, R., Wilson, R., Liepert, B., and Cherubini, P.: On the “Divergence
Problem” in Northern Forests: A review of the the tree-ring evidence and
possible causes, Global Planet. Change, 60, 289–305, 2008.
Dee, S., Emile-Geay, J., Evans, M., Allam, A., Steig, E., and Thompson, D.:
PRYSM: An open-source framework for PRoxY System Modeling, with applications
to oxygen-isotope systems, Journal of Advances in Modeling Earth Systems, 7,
1220–1247, 2015.
Dee, S., Steiger, N. J., Emile-Geay, J., and Hakim, G. J.: On the utility of
proxy system models for estimating climate states over the common era,
Journal of Advances in Modeling Earth Systems, 8, 1164–1179, 2016.Dirren, S. and Hakim, C.: Toward the assimilation of time-averaged
observations, Geophys. Res. Lett., 32, L04804, 10.1029/2004GL021444, 2005.Dubinkina, S. and Goosse, H.: An assessment of particle filtering methods and
nudging for climate state reconstructions, Clim. Past, 9, 1141–1152,
10.5194/cp-9-1141-2013, 2013.Epstein, S. and Mayeda, T.: Variation of O18 content of waters from
natural sources, Geochim. Cosmochim. Ac., 4, 213–224, 1953.
Evans, M. N., Tolwinski-Ward, S. E., Thompson, D. M., and Anchukaitis, K. J.:
Applications of proxy system modeling in high resolution paleoclimatology,
Quaternary Sci. Rev., 76, 16–28, 2013.Evans, M. N., Smerdon, J. E., Kaplan, A., Tolwinski-Ward, S. E., and
González-Rouco, J. F.: Climate field reconstruction uncertainty arising
from multivariate and nonlinear properties of predictors, Goephys. Res.
Lett., 41, 9127–9134, 10.1002/2014GL062063, 2014.
Gaspari, G. and Cohn, S.: Construction of correlation functions in two and
three dimensions, Q. J. Roy. Meteor. Soc., 125, 723–757, 1999.Goodkin, N. F., Hughen, K. A., Curry, W. B., Doney, S. C., and Ostermann, D.
R.: Sea surface temperature and salinity variability at Bermuda during the
end of the Little Ice Age, Paleoceanography, 23, PA3203, 10.1029/2007PA001532,
2008.
Goosse, H., Renssen, H., Timmermann, A., Bradley, R., and Mann, M.: Using
paleoclimate proxy-data to select optimal realisations in an ensemble of
simulations of the climate of the past millennium, Clim. Dynam., 27,
165–184, 2006.Goosse, H., Crespin, E., de Montety, A., Mann, M., Renssen, H., and
Timmermann, A.: Reconstructing surface temperature changes over the past 600
years using climate model simulations with data assimilation, J. Geophys.
Res., 115, D09108, 10.1029/2009JD012737, 2010.
Goosse, H., Crespin, E., Dubinkina, S., Loutre, M., Mann, M., Renssen, H.,
Sallaz-Damaz, Y., and Shindell, D.: The role of forcing and internal dynamics
in explaining the “Medieval Climate Anomaly”, Clim. Dynam., 39, 2847–2866,
2012.
Hartmann, D. L., Klein Tank, A. M. G., Rusticucci, M., Alexander, L. V.,
Brönnimann, S., Charabi, F., Dentener, F. J., Dlugokencky, E. J.,
Easterling, D. R., Kaplan, A., Soden, B. J., Thorne, P. W., Wild, M., and
Zhai, P. M.: Observations: Atmosphere and Surface, in: Climate Change 2013:
The physical science basis. Contribution of Working Group I to the Fifth
Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge
University Press, Cambridge, UK and New York, NY, USA, 2013.
Hoffmann, G., Werner, M., and Heimann, M.: Water isotope module of the ECHAM
atmospheric general circulation model: A study on timescales from days to
several years, J. Geophys. Res., 103, 16871–16896, 1998.
Houtekamer, P. L. and Zhang, F., Review of the ensemble Kalman filter for
atmospheric data assimilation, Mon. Weather Rev., 144, 4489–4532, 2016.
Hughes, M. and Ammann, C.: The future of the past – an earth system
framework for high resolution paleoclimatology: editorial essay, Climatic
Change, 94, 247–259, 2009.
Huntley, H. and Hakim, G.: Assimilation of time-average observations in a
quasi-geostrophic atmospheric jet model, Clim. Dynam., 35, 995–1009, 2010.
Joussaume, S., Sadourny, R., and Jouzel, J.: A general circulation model of
water isotope cycles in the atmosphere, Nature, 311, 24–29, 1984.Jouzel, J., Russell, G. L., Suozzo, R. J., Koster, R. D., White, J. W. C.,
and Broecker, W. S.: Simulations of the HDO and H218O Atmospheric
cycles using the NASA GISS General Circulation Model: The seasonal cycle for
present-day conditions, J. Geophys. Res., 92, 14739–14760, 1987.
Julliet-Leclerc, A. and Schmidt, G.: A calibration of the oxygen isotope
paleothermometer of coral aragonite from Porites, Geophys. Res. Lett., 28,
4135–4138, 2001.Lee, J.-E., Fung, I., DePaolo, D., and Henning, C.: Analysis of the global
distribution of water isotopes using the NCAR atmospheric general circulation
model, J. Geophys, Res., 112, D16306, 10.1029/2006JD007657, 2007.LeGrande, A. and Schmidt, G.: Global gridded data set of the oxygen isotopic
composition in seawater, Geophys. Res. Lett., 33, L12604, 10.1029/2006GL026011,
2006.LeGrande, A. N. and Schmidt, G. A.: Sources of Holocene variability of oxygen
isotopes in paleoclimate archives, Clim. Past, 5, 441–455,
10.5194/cp-5-441-2009, 2009.
Liu, G., Kojima, K., Yoshimura, K., Okai, T, Suzuki, A., Oki, T., Siringan,
F., Yoneda, M., and Kawahata, H.: A model-based test of accuracy of seawater
oxygen isotope ratio record derived from a coral dual proxy method at
southeastern Luzon Island, the Philippines, J. Geophys. Res.-Biogeo., 118,
853–859, 2013.Liu, G., Kojima, K., Yoshimura, K., and Oka, A.: Proxy interpretation of
coral-recorded seawater 18O using 1-D model forced by
isotope-incorporated GCM in tropical oceanic regions, J. Geophys.
Res.-Atmos., 119, 12021–12033, 10.1002/2014JD021583, 2014.
Managave, S. R., Sheshshayee, M. S., Ramesh, R., Borgaonkar, H. P., Shad, S.
K., and Bhattacharyya, A.: Response of cellulose oxygen isotope values of
teak trees in differing monsoon environments to monsoon rainfall,
Dendrochronologia, 29, 89–97, 2011.
Mann, M., Zhang, Z., Hughes, M., Bradley, R., Miller, S., Rutherford, S., and
Ni, F.: Proxy-based reconstructions of hemispheric and global surface
temperature variations over the past two millennia, P. Natl. Acad. Sci. USA,
105, 13252–13257, 2008.Mathiot, P., Goosse, H., Crosta, X., Stenni, B., Braida, M., Renssen, H., Van
Meerbeeck, C. J., Masson-Delmotte, V., Mairesse, A., and Dubinkina, S.: Using
data assimilation to investigate the causes of Southern Hemisphere high
latitude cooling from 10 to 8 ka BP, Clim. Past, 9, 887–901,
10.5194/cp-9-887-2013, 2013.Noone, D. and Simoonds, I., Associations between δ18O of water and
climate parameters in a simulation of atmospheric circulation for 1979–95,
J. Climate, 15, 3150–3169, 2002.
North, G., Bell, T. L., and Cahalan, R. F., Sampling errors in the estimation
of empirical orthogonal functions, Mon. Weather Rev., 110, 699–706, 1982.
Okazaki, A. and Yoshimura, K.: Development of stable water isotope
incorporated atmosphere-land coupled model MIROC5, in preparation,
2017.
PAGES 2k Consortium, Continental-scale temperature variability during the
past wto millennia, Nat. Geosci., 6, 339–346, 2013.
Peterson, T. C. and Vose, R. S.: An overview of the global historical
climatology network temperature database, B. Am. Meteorol. Soc., 78,
2837–2849, 1997.
Rabier, F., Järvinen, H., Klinker, E., Mahfouf, J.-F., and Simmons, A.:
The ECMWF operational implementation of four-dimensional variational
assimilation. I: Experimental results with simplified physics, Q. J. Roy.
Meteor. Soc., 126, 1143–1170, 2000.
Rasmusson, E. M. and Capenter, T. H.: The relationship between eastern
Equatorial Pacific sea surface temperatures and rainfall over India and Sri
Lanka, Mon. Weather Rev., 111, 517–528, 1983.Rayner, N. A., Parker, D. E., Horton, E. B., Folland, C. K., Alexander, L.
V., Rowell, D. P., Kent, E. C., and Kaplan, A.: Global analyses of sea
surface temperature, sea ice, and night marine air temperature since the late
nineteenth century, J. Geophys. Res., 108, D144407, 10.1029/2002JD002670, 2003.Rhodes, R. H., Bertler, N. A. N., Baker, J. A., Steen-Larsen, H. C., Sneed,
S. B., Morgenstern, U., and Johnsen, S. J.: Little Ice Age climate and
oceanic conditions of the Ross Sea, Antarctica from a coastal ice core
record, Clim. Past, 8, 1223–1238, 10.5194/cp-8-1223-2012, 2012.Risi, C., Bony, S., Vimeux, F., and Jouzel, J.: Water-stable isotopes in the
LMDZ4 general circulation model: Model evaluation for present-day and past
climates and applications to climatic interpretations of tropical isotopic
records, J. Geophys. Res., 115, D12118, 10.1029/2009JD013255, 2010.
Roden, J., Lin, G., and Ehleringer, J.: A mechanistic model for
interpretation of hydrogen and oxygen isotope ratios in tree-ring cellulose,
Geochim. Cosmochim. Ac., 64, 21–35, 2000.Sano, M., Xu, C., and Nakatsuka, T.: A 300-year Vietnam hydroclimate and ENSO
variability record reconstructed from tree ring δ18O, J. Geophys.
Res., 117, D12115, 10.1029/2012JD017749, 2012.Schmidt, G., Hoffmann, G., Shindell, D., and Hu, Y.: Modeling atmospheric
stable isotopes and the potential for constraining cloud processes and
staratosphere-troposphere water exchange, J. Geophys. Res., 110, D21314,
10.1029/2005JD005790,
2005.Schmidt, G., LeGrande, A., and Hoffmann, G.: Water isotope expressions of
intrinsic and forced variability in coupled ocean-atmosphere model, J.
Geophys. Res., 112, D10103, 10.1029/2006JD007781, 2007.Schneider, D. P. and Noone, D. C.: Spatial covariance of water isotope
records in a global netweok of ice cores spanning twentieth-century climate
change, J. Geophys. Res., 112, D18105, 10.1029/2007JD008652, 2007.
Schotterer, U., Stichler, W., and Ginot, P.: The influence of
post-depositional effects on ice core studies: Examples from the Alps, Andes,
and Altai, in Earth Paleoenvironments: Records Preserved in Mid- and
Low-Latitude Glaciers, 39–59, Kluwer Acad, Dordrecht, the Netherlands, 2004.
Steiger, N., Hakim, G., Steig, E., Battisti, D., and Roe, G.: Assimilation of
Time-Averaged Pseudoproxies for Climate Reconstruction, J. Climate, 27,
426–441, 2014.
Taylor, K. E., Stouffer, R. J., and Meehl, G.: An overview of CMIP5 and the
experiment design, B. Am. Meteorol. Soc., 93, 485–498, 2007.
Takeuchi, N., Fujita, K., Aizen, V. B., Narama, C., Yokoyama, Y., Okamoto,
S., Naoki, K., and Kobota, J.: The disappearance of glaciers in the Tien Shan
Mountains in Central Asia at the end of Pleistocene, Quaternary Sci. Rev.,
103, 26–33, 2014.Thompson, D. M., Ault, T. R., Evans, M. N., Cole, J. E., and Emile-Geay, J.:
Comparison of observed and simulated tropical climate trends using a forward
model of coral δ18O, Geophys. Res. Lett., 38, L14706, 10.1029/2011GL048224,
2011.
van der Schrier, G. and Barkmeijer, J.: Bjerknes' hypothesis on the coldness
during AD 1790–1820 revisited, Clim. Dynam., 25, 537–553, 2005.
van Leeuwen, P. J.: Particle filtering in geophysical systems, Mon. Weather
Rev., 137, 4089–4114, 2009.
von Storch, H., Cubasch, U., Gonzalez-Rouco, J. F., Jones, J. M., Voss, R.,
Widmann, M., and Zorita, E.: Combining paleoclimatic eviedence and GCMs by
means of data assimilation though upscaling and nudging (DATUN), Proc. 11th
Symposium on Global Climate Change Studies, AMS Long Beach, CA, 2000.
Watanabe, M., Suzuki, T., O'ishi, R., Komuro, Y., Watanabe, S., Emori, S.,
Takemura, T., Chikira, M., Ogura, T., Sekiguchi, M., Takata, K., Yamazaki,
D., Yokohota, T., Nozawa, T., Hasumi, H., Tatebe, H., and Kimoto, M.:
Improved climate simulation by MIROC5: Mean States, Variability, and Climate
Sensitivity, J. Climate, 23, 6312–6335, 2010.Werner, M., Langebroek, P., Carlsen, T., Herold, M., and Lohmann, G.: Stable
water isotopes in the ECHAM5 general circulation model: Toward
high-resolution isotope modeling on a global scale, J. Geophys. Res., 116,
D15109, 10.1029/2011JD015681, 2011.
Whitaker, J. S. and Hamill, T. M.: Ensemble data assimilation without
perturbed observations, Mon. Weather Rev., 130, 1913–1924, 2002.Widmann, M., Goosse, H., van der Schrier, G., Schnur, R., and Barkmeijer, J.:
Using data assimilation to study extratropical Northern Hemisphere climate
over the last millennium, Clim. Past, 6, 627–644, 10.5194/cp-6-627-2010,
2010.Xu, C., Sano, M., and Nakatsuka, T.: Tree ring cellulose δ18O of
Fokienia hodginsii in northern Laos: A promising proxy to reconstruct ENSO?,
J. Geophys. Res., 116, D245109, 10.1029/2011JD016694, 2011.
Xu, C., Zheng, H., Nakatsuka, T., and Sano, M.: Oxygen isotope signatures
preserved in tree ring cellulose as a proxy for April-September precipitation
in Fujian, the subtropical region of southeast China, J. Geophys. Res-Atmos.,
118, 12805–12815, 2013.Xu, C., Pumijumnong, N., Nakatsuka, T., Sano, M., and Li, Z.: A tree-ring
cellulose δ18O-based July-October precipitation reconstruction
since AD 1828, northwest Thailand, J. Hydrol., 529, 422–441, 2015.Yoshimura, K., Kanamitsu, M., Noone, D., and Oki, T.: Historical isotope
simulation using Reanalysis atmospheric data, J. Geophys, Res., 113, D19108,
10.1029/2008JD010074,
2008.
Yoshimura, K., Miyoshi, T., and Kanamitsu, M.: Observation system simulation
experiments using water vapor isotope information, J. Goephys, Res., 119,
7842–7862, 2014.
Young, G. H. F., Loader, N. J., McCarroll, D., Bale, R. J., Demmler, J. C.,
Miles, D., Nayling, N., Rinne, K. T., Robertson, I., Watts, C., and Whitney,
M.: Oxygen stable isotope ratios from British oak tree-rings provide a strong
and consistent record of past changes in summer rainfall, Clim. Dynam., 45,
3609–3622, 2015.