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PALEOCEANOGRAPHY, VOL. 23, PA2221, doi:10.1029/2007PA001461, 2008
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On the definition of seasons in paleoclimate
simulations with orbital forcing
Oliver Timm,1 Axel Timmermann,1 Ayako Abe-Ouchi,2,3 Fuyuki Saito,3
and Tomonori Segawa3
Received 29 March 2007; revised 1 March 2008; accepted 25 March 2008; published 26 June 2008.
[1] Orbital forcing is a major driver of climate variability on timescales of 10,000 to 100,000 years. Changes in
the orbital parameters cause variations in the length of the seasons by several days. Consequently, models using
a fixed present-day calendar result in biased paleoseasons, especially in boreal autumn when the vernal equinox
is used as an anchor point. The bias is estimated for temperatures and precipitation in a transient model
simulation over the last 21,000 years and an accelerated simulation over the last 129,000 years. The largest
differences of up to 4 K occur over the continents in high latitudes. Precipitation estimates are mostly affected in
the low latitudes. The time-dependent bias is large enough to modify the temporal characteristics of temperature
and precipitation indices. It is discussed to what extent the bias in one season is distorting comparisons between
models and paleoproxies. The bias has minor implications for proxy-model comparisons in general. However,
proxies of monsoon activity should be compared with fixed angular seasons. For process studies and climate
sensitivity studies the use of fixed angular seasons is imperative.
Citation: Timm, O., A. Timmermann, A. Abe-Ouchi, F. Saito, and T. Segawa (2008), On the definition of seasons in paleoclimate
simulations with orbital forcing, Paleoceanography, 23, PA2221, doi:10.1029/2007PA001461.
1. Introduction
[2] Since the pioneering work of Milankovitch [1941],
Veeh and Chappell [1970], Hays et al. [1976], and Imbrie
and Imbrie [1980] among others little doubt is left that
orbitally driven insolation anomalies force climate variations on orbital timescales. The Milankovitch cycles have
been found in various climate records from marine sediment
cores [Hays et al., 1976; Crowley and North, 1991], ice
cores [Genthon et al., 1987; EPICA Community Members,
2004], and speleothems [Thompson et al., 1974; Cruz et al.,
2005]. These data clearly demonstrate that the climate
system is responding to the external forcing. However, the
detailed amplification mechanisms and feedbacks within the
climate system are still unresolved [Raymo and Nisancioglu,
2003; Huybers and Wunsch, 2005; Huybers, 2006; Roe,
2006].
[3] In order to fully understand those processes, climate
models are needed that are capable of simulating the climate
evolution over full glacial-interglacial cycles. Such transient
simulations will complement our understanding of orbitalscale climate change that is based on the existing time slice
experiments, such as the recent PMIP2 simulations [Cane et
al., 2006; Braconnot et al., 2007a, 2007b], and time series
from paleoproxies.
1
International Pacific Research Center, SOEST, University of Hawai’i
at Manoa, Honolulu, Hawaii, USA.
2
Center for Climate System Research, University of Tokyo, Kashiwa,
Japan.
3
Frontier Research Center for Global Change, Japan Agency for
Marine-Earth Science and Technology, Yokohama, Japan.
Copyright 2008 by the American Geophysical Union.
0883-8305/08/2007PA001461$12.00
[4] The variations of the three orbital parameters (eccentricity, obliquity, and precession) produce a complex pattern
in the latitudinal and seasonal insolation anomalies [e.g.,
Berger et al., 1993]. The combined effect of eccentricity and
precession dominates the changes in the daily to seasonal
mean insolation in most latitudes [Berger et al., 1993].
Kepler’s second law states that the area Df covered by the
connecting line between Earth and Sun in a given time Dt is
constant (see Figure 1). Hence the angular velocity of the
Earth is not constant throughout a year. Moreover, the
angular velocity depends on the phase of the precessional
cycle.
[5] In this paper we will discuss the effects of the
precessional forcing on the definition of seasons in paleoclimate model simulations. Astronomical seasons are defined by the 90° segments between the winter solstice (WS),
vernal equinox (VE), summer solstice (SS), and autumnal
equinox (AE) (Figure 1). The present-day calendar seasons
used in climate studies are closely tied to the astronomical
seasons. (‘‘Meteorological seasons’’ begin about 3 weeks
earlier in order to describe more accurate the differences
observed in the weather, flora and fauna of extratropical
regions). If the same calendar days define the seasons
(hereafter referred to as ‘‘fixed calendar’’ seasons) in
paleosimulations with precessional forcing, a direct comparison between the seasons from present day and, for example,
the early Holocene would be biased because of the shift of
the fixed calendar seasons with respect to the astronomical
seasons (for details, see Joussaume and Braconnot [1997]).
The problem is illustrated for 10,000 years before present
(B.P.) in Figure 1. At present, the distance Earth-Sun is
smaller in boreal winter than in summer (hereinafter all
seasons are defined for the Northern Hemisphere unless the
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Figure 1. Sketch of the orbital configuration at (a) present and (b) 12,000 B.P. The astronomical seasons
are marked by the vernal equinox (VE), summer solstice (SS), autumnal equinox (AE), and winter
solstice (WS). The position of Sun and Earth are marked with S and E, respectively. At the indicated true
longitude position l the Earth is closer to the Sun in Figure 1b than in Figure 1a. For a given time interval
Dt, the shaded areas Df in Figures 1a and 1b are equal according to Kepler’s second law. Hence the angle
Dl in Figure 1a is smaller than Dl in Figure 1b. At 12,000 B.P., the astronomically defined boreal
spring/summer season was shorter than the spring/summer season at present.
term ‘‘austral’’ is used to indicate Southern Hemisphere
seasons). Hence the increment in the true longitude angle
Dl during a given time Dt (e.g., 1 day) is larger in winter
than in summer, and the present summer season contains
more days than the winter season. At the beginning of
the Holocene the Northern Hemisphere experienced more
days with winter-like insolation. Averages of insolation
using the fixed calendar seasons from 10,000 B.P. will
include insolations of different true longitude ranges along
the Earth’s orbit [Berger, 1978; Berger et al., 1993]. A
‘‘fixed angular’’ season, which covers a constant segement
of the orbit, is to be preferred to the fixed calendar
season [Milankovitch, 1930; Thomson, 1995; Joussaume
and Braconnot, 1997; Pollard and Reusch, 2002]. Note that
the terms fixed calendar (fixed angular) are equivalent to the
‘‘classical’’ (‘‘angular’’) season used by Joussaume and
Braconnot [1997].
[6] A few model studies describe precisely how the
seasonal averages are calculated. For example, Lorenz et
al. [2006] and Yoshimori et al. [2001] show insolation
anomalies using fixed angular insolation data, whereas
Liu et al. [2003] present fixed calendar anomalies. These
two ways of mapping insolation anomalies in a monthlatitude plane exhibit large differences, especially in the
high southern latitudes in austral spring. The mid-Holocene
austral spring anomalies of Liu et al. [2003, Figure 1] are
as large as 48 W m2; in the work of Lorenz et al. [2006]
they reach only 10 W m2. This severe bias in the
insolation forcing could lead to significantly different model
interpretations.
[7] With the growing number of transient paleosimulations
[Jackson and Broccoli, 2003; Felis et al., 2004; Lorenz and
Lohmann, 2004; Tuenter et al., 2005; Lorenz et al., 2006;
Renssen et al., 2005; Charbit et al., 2005; Lunt et al., 2006;
Marsh et al., 2006; Timmermann et al., 2007; Timm and
Timmermann, 2007], an estimate of the time-dependent
biases due to the fixed calendar becomes important.
[8] In this paper we present a comparison of the differences between fixed calendar day seasons and fixed angular
seasons. A transient simulation with the Earth system model
of intermediate complexity ECBilt-CLIO covering the last
21,000 years, and an accelerated simulation over the last
129,000 years are used to study the effects of the seasonal
definition on the derived time series of temperatures and
precipitation. A method is presented to estimate the differences resulting from the shifts in the seasons, in which only
a daily resolution annual cycle from a preindustrial control
simulation is needed. The discussion focuses on the consequences for the climatic interpretation of seasonal model
results and the model-proxy comparison. As an example, we
compare the 129,000-year simulation with proxies of the
Asian Monsoon circulation [Wang et al., 2001; Dykoski et
al., 2005; Wang et al., 2005] and the South Brazil Monsoon
[Cruz et al., 2005].
2. Model and Methods
[9] The ECBilt-CLIO model (version 3) is an Earth
system model of intermediate complexity (EMIC)
[Opsteegh et al., 1998; Goosse and Fichefet, 1999]. It
consists of three mutually coupled subsystems: a simplified
three-layer global atmosphere, a 3-D global ocean and a
thermodynamic-dynamic sea ice component. The latest
version of this EMIC model further includes a terrestrial
vegetation and a biogeochemical carbon cycle subsystem,
known as LOVECLIM (here, we will still use the old name,
which avoids confusion about the model version and the
complexity of the model).
[10] The atmospheric part is able to reproduce the largescale dynamics of the atmosphere. In the extratropical
regions, ‘‘weather’’ variability is well simulated, whereas
the tropical intraseasonal and interannual variability is
underestimated. A set of simplified physical parameterizations are implemented for the calculation of shortwave and
longwave radiation, clouds, and precipitation. The radiation
scheme uses a linearization with respect to present-day
conditions. The seasonally and spatially varying cloud
cover climatology is prescribed in the model.
[11] The ocean component CLIO simulates the threedimensional ocean circulation, temperature, and salinity
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distribution. It further simulates the thermodynamic and
dynamic properties of sea ice in the high latitudes. The
horizontal resolution is 3° 3°. In the vertical direction,
the ocean consists of 20 levels (13 representing the upper
1000 m). In our simulations the effect of glacial-interglacial
sea level changes on the bathymetry and on the seawater
salinity is neglected. The Bering Strait is closed in the
simulations.
[12] The three components of ECBilt-CLIO are coupled
by exchange of momentum, heat, and freshwater. Soil
moisture and river runoff into the ocean are calculated in
order to close the hydrological cycle. A small correction in
the freshwater flux is applied over the oceans in order to
correct the excessive precipitation over the North Atlantic
and Arctic.
[13] Ice sheet forcing is prescribed in the simulations
through temporal changes in the orography and surface
albedo. The anomalies follow the time-dependent ice sheet
reconstruction ICE4G [Peltier, 1994] in the 21,000-year
simulation. For the 129,000-year-long simulation, the ice
sheet modeling results from Abe-Ouchi et al. [2007] are
used. Time-varying atmospheric CO2, CH4 and N2O concentrations are prescribed in the model. The CO2 data were
taken from the Antarctic ice core Taylor Dome [Indermühle
et al., 1999; Smith et al., 1999]. CH4 and N2O are data from
samples in the GISP2 ice core [Brook et al., 1996; Sowers et
al., 2003]. Note that in the 129,000-year-long simulation
only CO2 was time-dependent, whereas N2O, CH4 were
fixed to preindustrial levels.
[14] Most important for this study is the orbital forcing.
The daily mean irradiance is calculated following Berger
[1978]. Note, that ECBilt-CLIO applies a 360-day year.
The transient forcing for the 21,000-year simulation and the
accelerated forcing technique, which was applied in the
129,000-year simulation, are described in detail by Timm
and Timmermann [2007].
[15] ECBilt-CLIO per default only generates fixed calendar seasonal output. The seasons are defined for present-day
orbital parameters. A year is divided into 12 months with
30 days, in which the vernal equinox (VE) (see Figure 1) is
tied to day 81 in the calendar year. The 3-month averages
December – January – February (DJF), March – April – May
(MAM), June – July August (JJA), September – October –
November (SON) form the boreal winter, spring, summer,
and autumn seasons, respectively. Note these seasons do not
match up with the astronomical seasons with 90° segments
of the orbit.
[16] In order to obtain fixed angular seasons, we saved
10 years of daily atmospheric output every 1000 years
(every 2000 years in the 129,000-year simulation). We used
the present-day seasons of the model and identified the true
longitude l of the Earth (the angle between Earth and VE)
for the first day in each season. Keeping these angular
markers fixed, the calendar days in each fixed angular
season can be determined for the orbital configurations
between 129,000 and 0 years B.P.
[17] A formal description of the seasonal averaging
operations can be written in simple algebraic form (see
Appendix A). There are two terms contributing to the
differences between variables averaged over fixed calendar
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and fixed angular seasons. First, there is a direct effect by
the shift in the averaging interval. In the presence of a
pronounced annual cycle, the shift leads to large differences,
even if the climate state was unchanged in the paleoclimate
simulation (term d0(t) in equation (A5)). Second, a change
in the annual cycle in the paleosimulation can introduce an
~
additional bias (term d(t)).
3. Results
[18] The consequences of the orbital parameter changes
on the length of the seasons are illustrated in Figure 2. For
present-day and a 360-day year, the seasons are all 90 days
long in the model. The length of angular seasons changed
over the 21,000 years by up to ±6 days. The maximum
winter length is reached at about 10,000 B.P. Spring and
autumn are less variable (±4 days). As noted by Joussaume
and Braconnot [1997], the length changes result in shifts of
the seasons. Figure 2b highlights the shift of the fixed
angular season compared with the fixed calendar seasons
for the 360-day model year. The angular spring season is
only marginally shifted relative to the fixed calendar spring.
This is due to the anchor point VE that is fixed to calendar
day 81. The astronomical start dates of autumn and winter
shift by a maximum of 6 days at 12,000 B.P. and 9000 B.P.,
respectively. The fixed calendar summer (autumn) therefore
results in a seasonal average that is biased toward autumn
(winter) conditions. This is illustrated in Figure 3 by
showing the mean annual cycle of temperature and insolation for 10,000 B.P. and 0 B.P. together with the two
different autumn season segments.
3.1. Spatial Pattern
[19] The effects on the autumn averaged temperatures are
readily noted in Figure 4a. The 2-m air temperature differences d(t) between the fixed calendar and fixed angular
autumn are averaged over 9000 – 11,000 B.P., during which
the seasons have maximum phase shifts. The Northern
Hemisphere (Southern Hemisphere) temperatures of the
fixed calendar autumn have a negative (positive) bias
because days with winter-like insolation become part of
the averaging interval, which leads to lower autumn temperatures compared to the fixed angular season in the high
northern latitudes. The opposite bias is observed over the
Southern Hemisphere, where the austral calendar spring
season is including austral summer conditions. The largest
differences occur over the continents. The differences are
less over the ocean, as a result of the larger heat capacity,
which reduces the annual cycle amplitude. Shifts in the
season are therefore less severe. The estimation of the
differences resulting from the pure phase shift do(t)
(equation (A5)) are shown in Figure 4b. The spatial structure of do(t) and d(t) are very similar and the magnitudes
of the pattern are in close agreement.
[20] The differences in the precipitation of the fixed
calendar and fixed angular autumn show a dipole structure
with a negative (positive) bias north (south) of the equator
in the low latitudes (Figure 4c). Large biases occur over
Africa, India, the maritime continent, and South America.
The phase shift in the calendar season with respect to the
angular season is associated with seasonal biases of the
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Figure 2. Changes in the length of the fixed angular seasons in the (a) 21,000-year paleoclimate
simulation and (b) start/end days of the fixed angular seasons. The fixed angular seasons have been
defined according to the present definition of the seasons in the 360-day model year. Symbols in Figure 2a
represent boreal winter (circles), spring (squares), summer (upward triangle), and autumn (downward
triangle). In Figure 2b the lines indicate the beginning of the four seasons in the 360-day model year.
insolation. Consequently, the fixed calendar autumn precipitation is biased toward the early boreal winter (early austral
summer) Monsoon in the Northern Hemisphere (Southern
Hemisphere). The close correspondence between d(t) in
Figure 4c and do(t) in Figure 4d illustrates that the bias in
the fixed calendar season can be significantly reduced by
knowledge of the present-day annual precipitation cycle
(with daily resolution) and calculations of the operator
[Ac Aa(t)] (see Appendix A).
3.2. Differences Over the Last 21,000 Years
[21] Figure 5 demonstrates that the time-dependent bias
can have a significant influence on the temporal evolution
of autumn temperatures. This is illustrated by the time series
of zonally averaged 2-m air temperatures at 60°N. Compared with the LGM-Holocene temperature differences of
12 K, the bias of 2 K in the fixed calendar autumn is
relatively small. However, during the Holocene the season
definition changes drastically the temporal characteristics. A
clear early Holocene thermal maximum is only observed in
the fixed angular season. Subsequently, a negative trend is
noticeable over the Holocene in the fixed angular autumn
but not in the fixed calendar autumn. The opposite effect,
although weaker, is observed over the Southern Hemisphere
at 70°S.
[22] Figure 6 illustrates the effect of the season definition
on the precipitation over the Indian Monsoon region. The
biases are largest in the late part of the wet season of the
Indian summer monsoon (i.e., autumn). The magnitude of
the maximum bias at about 11,000 – 9000 B.P. is comparable to the full LGM-Holocene difference. Consequently, the
time series of the climate evolution exhibit two different
signatures. The maximum precipitation is reached at
10,000– 8000 B.P. for fixed angular autumn, but this feature
Figure 3. Example illustration of the differences in the
two season definitions for 10,000 B.P. Shown are the annual
cycles of insolation and zonally averaged 2-m air temperatures at 60°N for 10,000 B.P. (bold solid lines) and present
(bold dashed lines). The different shadings in the top and
bottom mark the fixed angular seasons at 10,000 B.P. and the
fixed calendar seasons. The effect of the shift in the seasons
on the averaging is depicted for the autumn season. Dashed
vertical lines highlight the shift of the fixed calendar autumn
relative to the fixed angular autumn. The corresponding
autumn mean temperatures at 10,000 B.P. and insolation
values are given by the horizontal lines.
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Figure 4. Differences between the fixed angular and the fixed calendar (a and b) 2-m air temperatures
and (c and d) precipitation for the boreal autumn season in the early Holocene (11,000 – 9000 B.P.). In
Figures 4a and 4c the differences d(t) were estimated from 10 years of daily model output. In Figures 4b
and 4d the bias in the season (do (t), equation (A5)) was estimated from the daily annual cycle of a
preindustrial control run. Negative (positive) differences indicate a cold (warm) bias and more (less)
precipitation in the fixed calendar season. Contours in Figures 4a and 4b are in 0.5 K intervals, and in
Figures 4c and 4d they are in 5 cm a1 intervals.
is masked by the negative bias in the calendar season.
Consequently, the negative Holocene precipitation trend of
the Indian Monsoon is less pronounced in the calendar
season.
3.3. Differences in the Last 129,000 Years
[23] The 129,000-year-long simulation allows for an
exploration of the effects of the shifts in the seasons further
back in time; 100,000 years ago the eccentricity was much
larger than in the last 21,000 years (0.04 versus 0.02). This
leads to even more pronounced changes in the length and
shift of the seasons. The differences between fixed calendar
and fixed angular seasons over the last 129,000 years are
shown for the zonal mean temperatures (Figure 7). Strong
biases in the early part of the autumn temperature series at
60°N result in phase shifts of the maxima of the precessional cycle at 120,000, 100,000 and 80,000 B.P. At 70°S
the effect is less severe, where the differences between the
two season definitions result mainly in an overestimation of
the precessional cycles in the fixed calendar season because
of the systematic intrusion of austral summer days into the
averaging interval.
[24] The Indian Monsoon rain in autumn is most strongly
affected during the large precessional forcing cycles between 129,000 B.P. and 60,000 B.P. (Figure 8). The
increased precipitation periods during the times of increased
incoming insolation are underestimated in the fixed calendar
season. This leads also to a small phase shift in the timing of
the maxima.
3.4. Bias Correction
[25] Since we directly calculated the fixed angular and
fixed calendar seasonal averages from daily model data, we
estimate whether a posterior correction using only daily
output from a preindustrial control simulation according to
equation (A5) is feasible. It is clear from Figure 3 that the
preindustrial annual cycle and the annual cycle for a given
paleoyear must have similar form to achieve any reasonable
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Figure 5. Zonal mean 2-m air temperatures for boreal autumn over the last 21,000 years: (a) at 60°N
and (b) at 70°S. The fixed calendar season of the transient simulation is shown in black. Averages and
standard deviations recalculated from the 10-year daily data are shown: fixed calendar (red circles) and
fixed angular seasonal averages (green triangles).
correction. Note that a constant offset is canceled out by the
operator [Ac Aa(t)]. The differences d(t), which have
been calculated from the daily model data, are shown in
Figure 9 together with the estimates of d0(t). For the
zonally averaged temperatures at 60°N and 70°S, the time
series of d(t) and d0(t) are very similar. For the regional
precipitation index, significant differences between the
years 129,000 and 60,000 cannot fully be explained by
the shift of the seasons alone. For precipitation, the second~
ary effect of changes in the annual cycle (term d(t)
in
equation (A5)) contributes to the differences between the
fixed angular and fixed calendar seasons. But both for
temperature and precipitation, a first-order bias correction
~
is possible without taking into account d(t).
We note that
the application of this bias correction to GCM results should
be carefully tested. Since our model underestimates the
interannual variability and probably also the sytematic
changes in the tropical precipitation, the bias corrections
in the tropical precipitation may deteriorate in GCM applications. Larger sample sizes of 100 model years will be
needed to reduce the interannual variability. The bias
correction should then be compared with the results
obtained by the method of Pollard and Reusch [2002].
Berger, 1978; Joussaume and Braconnot, 1997]. Since the
VE is tied to the day 81 in the calendar year (March 21st in
ECBilt-Clio), the changing lengths of the seasons can
produce the largest phase shifts between the fixed angular
and fixed calendar seasons in summer and autumn. According to equation (A4), largest differences will result, where
phase shift are concurrent with large incremental changes
4. Discussion
[26] The examples described above highlight the differences between the two definitions of seasons. We noted that
our results are based on a model with a 360-day year. From
previous discussions of this issue [see Joussaume and
Braconnot, 1997], we expect no significant changes of
our results in models using a 365-day calendar year. On
the other hand, the choice of the vernal equinox as a anchor
point for the conversion from calendar days into the true
longitude l is of crucial importance [Milankovitch, 1930;
Figure 6. Simulated boreal autumn precipitation over the
Indian Monsoon region (10°N –20°N, 60°E –100°E). The
fixed calendar season of the transient simulation is shown in
black. Averages and standard deviations recalculated from
the 10-year daily data are shown: fixed calendar (red circles)
and fixed angular seasonal averages (green triangles).
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Figure 7. Simulated boreal autumn 2-m air temperatures. As in Figure 5 but for the autumn
temperatures in an accelerated transient simulation over the last 129,000 years: zonally averaged
(a) at 60°N and (b) at 70°S.
(i.e., extrema in the derivative of the annual cycle) during
the transition seasons in the annual cycle. For the extratropical temperatures this is clearly the case in spring and
autumn. Therefore, the largest changes are expected for
autumn. Here, we will discuss the importance of these
differences for paleoclimatic studies.
4.1. Model-Proxy Comparison
[27] For comparisons between model and proxy data the
exact definition of the model season is likely to be of minor
importance. Many paleoproxies are interpreted as annual
mean signals or a weighted mean of the seasons. The
prominent ice core proxies from Antarctica (Byrd [Blunier
et al., 1998], Vostok [Petit et al., 1999], Taylor Dome [Steig
et al., 1998], Dome Fuji [Watanabe et al., 2003], EPICA
[EPICA Community Members, 2004]) are often interpreted
as annual mean signals, even though the estimation of their
response function is associated with large uncertainties. For
Antarctic ice cores, even the present-day annual cycle of
precipitation can only be estimated with large standard
deviations [Cullather et al., 1998; Reijmer et al., 2002].
Moreover, the temporal evolution of the hydrological cycle
has most likely experienced significant changes during
glacial-interglacial cycles. These reasons prohibit a strict
comparison of a single model season like autumn with ice
core records from Antarctica. The bias introduced by the
fixed calendar season appears to be less important than the
uncertainties in the response function of the Antarctic ice
core signals. For Greenland ice cores (e.g., GRIP [GRIP
Members, 1993], GISP2 [Grootes et al., 1993], NGRIP
[NGRIP Members, 2004]) the estimation of climatological
annual cycles of precipitation and net accumulation are
somewhat better constrained [Ohmura and Reeh, 1991;
Robasky and Bromwich, 1994; Calanca, 1994; Bromwich
et al., 1998; Cullather et al., 2000]. Some model studies
suggest that Greenland ice cores represent more the warm
season rather than the cold season and that changes in the
annual precipitation cycle have occurred over the last
glacial-interglacial cycle [Werner, 2000; Werner et al.,
2000]. The existing data hence indicate that year-round
accumulation occurs over central Greenland. Ice core proxies from Greenland should be interpreted as annual mean
signals with a moderate bias toward the warm seasons. A
precise understanding of the response function is considered
more important than the exact definition of the model
Figure 8. Simulated boreal autumn precipitation over the
Indian Monsoon region (10°N –20°N, 60°E – 100°E). As in
Figure 6 but for the accelerated transient simulation over the
last 129,000 years.
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Figure 9. Calculated differences between fixed calendar
and fixed angular boreal autumn season: (a) zonally
averaged 2-m air temperature 60°N, (b) zonally averaged
2-m air temperature 70°S, and (c) Indian Monsoon
precipitation. The differences d(t) (equation (A5)) are
shown in red (solid circles). The estimated biases due to the
pure shift in seasons given a fixed preindustrial annual cycle
(d 0(t)) are shown in black (open circles).
seasons for comparisons between Greenland proxies and
model data.
[28] Marine SST proxies like Mg/Ca, alkenone, planktic
foraminifera have the potential to reconstruct annual mean
SST as well as seasonal climate signals [Mix et al., 2001;
Kucera et al., 2005]. However, proxies from marine sediment cores can have a seasonal preference for summer/
autumn [Stott et al., 2004]. Large seasonal cycles in the
primary production, which is largely controlled by seasonality in shortwave radiation and wind stress related upwelling in the ocean, suggest that marine proxies reflect some
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preferred seasons rather than equally weighted seasons. The
seasonal summer/autumn biases derived above are relatively
small in low-latitude SSTs because of the larger heat
capacities and the smaller annual cycle. Therefore, we argue
that fixed calendar seasons can still be used in marine
proxy-model comparisons.
[29] Speleothem proxies that represent changes in the
monsoonal circulation and precipitation are proxies with a
strong seasonal response function [Wang et al., 2001; Sinha
et al., 2005; Cruz et al., 2005; Dykoski et al., 2005]. The
d18O of tropical speleothems is interpreted as a mixture of
two distinct d18O values in the precipitation. During the
winter (summer), d18O in precipitation is enriched (depleted)
over the Asian Monsoon region and South Brazil. The
rainfall ratio between both seasons defines the d 18O value
in the speleothem (as a first-order process). Our results have
shown that the late Indian summer monsoon in autumn is
critically depending on the definition of the season. To
avoid any biased interpretation of isotopic speleothem
records, comparisons with models should use the fixed
angular season, which is more closely following the
changes in the orbital configuration. However, even more
critical than the bias in the season definition is the question
how to define an appropriate index for the seasonality of
monsoonal precipitation. As can be seen from Figure 10b,
the use of different months to define the ratio between
summer and winter Monsoon precipitation can introduce
larger uncertainties than the definition of the calendar
seasons. It must be further noted that other important
characteristics of monsoonal climate variability are not
captured by this simple index. The length of the rain season,
the intensity and the onset of the season are important
features, which have direct environmental impact in the
monsoon regions.
[30] Irrespective of the freedom in the definition of the
seasonality index, our simulation and the proxies show a
clear coherence. The dominant signal is the precession. The
speleothem records of Hulu and Dongge Cave show the
large amplitudes during 129,000– 80,000 B.P. and a weaker
precessional signal between 80,000 – 20,000 B.P. in agreement with our simulation. The results support Kutzbach’s
hypothesis of a direct orbital forcing control of the Monsoon
systems [Kutzbach, 1981; Kutzbach and Otto-Bliesner,
1982]. Moreover, the proxies and the model show high
correlation in the region of the South American Monsoon.
Despite the uncertainties in the definition of our seasonality
index, phases agree rather well. The model ECBilt-CLIO
reproduces the interhemispheric antiphase correlation. A
more thorough analysis will be presented elsewhere.
4.2. Process Studies With Climate Models
[31] The definition of seasons will be most important in
process studies or sensitivity studies. The climate sensitivity
to orbital forcing is not well understood. Two factors
contribute to the difficulties. First, annual mean changes
in the incoming solar radiation are smaller than the seasonal
insolation changes, and second, feedbacks such as the sea
ice – albedo feedback in high latitudes strongly depend on
the season. The analysis of the climate sensitivity in
response to orbital forcing must take the seasonal aspects
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Figure 10. (a) Indian Monsoon seasonality index (ratio of June –July – August – September –October –
August/December – January – February – March – April – May (JJASON/DJFMAM) precipitation). The
indices based on fixed calendar seasons for the accelerated 129,000-year simulation are shown in black.
The open red (green) circles represent indices derived from the recalculated fixed calendar (fixed angular)
seasonal precipitation data (10-year averages). The speleothem d18O records from Hulu Cave [Wang et
al., 2001, 2005] (blue) and Dongge Cave [Dykoski et al., 2005] (cyan) are shown as a qualitative
comparison between model and proxies. (b) South Brazil Monsoon seasonality indices together with
the speleothem proxy record from Botuvera [Cruz et al., 2005] (cyan). Red (green) colors indicate the
precipitation ratio for fixed calendar (fixed angular) seasons. Lines with (without) open circles are the
ratios DJFMAM/JJASON (DJF/SON). Note that all isotope records have been multiplied with (1).
into account. Clearly, the biases in the fixed calendar
seasons depend on the choice of the anchor point. Whether
the vernal or austral equinox is tied to one day in the year,
has direct impact on the bias in the calendar season
[Joussaume and Braconnot, 1997]. This means that two
paleosimulations using different anchor points will produce
different fixed calendar climate anomalies with respect to a
preindustrial control state. Furthermore, the estimation of
the orbitally induced TOA insolation changes will be
different. To avoid misinterpretations of the climate sensitivity with respect to orbital forcing, seasonal climate
anomalies in the model must be defined as fixed angular
definition. Furthermore, the fixed calendar insolation
anomalies are not equivalent to the anomalies calculated
from ‘‘mid month’’ insolation of Berger [1978]. (Mid month
insolations are calculated for fixed true longitudes. Since the
fixed angular monthly means are averaged over a fixed true
longitude range, the numerical values of mid month insolations and fixed angular monthly means share the same
amplitude and phase characteristics on orbital scales.) The
mid month insolation is commonly presented in comparisons between paleoproxies and orbital forcing. To avoid
confusion clear definitions how the seasonal model outputs
have been calculated must be provided.
[32] Recently, a method to correct the bias in the fixed
calendar season has been proposed by Pollard and Reusch
[2002]. Their algorithm only needs the simulated annual
cycles based on fixed calendar monthly mean values and
interpolates onto a finer (daily) resolution. The interpolated
data are then averaged to form angular-fixed monthly/
seasonal averages. They found that their method experiences difficulties for tropical precipitation data, which have a
rather ‘‘unsmooth’’ annual cycle. Our method of correcting
fixed calendar model seasons estimates the phase shift –
induced bias from daily data of the mean present-day annual
cycle. The presented results suggest that this correction term
can significantly reduce the bias, but the method cannot take
into account changes in the annual mean cycle that project
onto the phase shift. The latter effect is less important for
temperature biases but it may have a significant impact on
precipitation. We have to emphasize that in GCM models
with more sophisticated cloud and precipitation parameterizations, the annual precipitation cycle may show larger
changes. This could increase the importance of the second~ on the total bias d(t). Further, both methods
ary effects d(t)
will require about 100 model years to calculate the annual
cycles without large uncertainties because of the large
interannual variability in tropical precipitation.
5. Summary
[33] Paleosimulations that use a fixed present-day calendar result in biased estimates of seasonal or monthly
mean quantities. When the PMIP convention is adopted
and the vernal equinox is used as an anchor point between
the astronomical angular coordinates and the calendar
days, the largest temperature biases occur in high latitudes
during the boreal autumn (austral spring) season.
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[34] The other seasons are not critically biased. However,
we suggest that monthly mean data should be considered
with great care regarding their definition. Precipitation
differences are largest in the low latitudes because of the
large amplitudes of the seasonal cycle in these regions. The
presented results demonstrate that the precise definition of
seasons is most important for intermodel comparisons,
dynamical process studies, and climate sensitivity studies.
The fixed angular season should be applied when seasonal
processes are under investigation. The use of fixed angular
season avoids spurious forcing and climate anomalies,
which bias the fixed calendar seasons. These biases have
already been studied in the context of time slice experiments
[Joussaume and Braconnot, 1997; Pollard and Reusch,
2002]. Here, it was demonstrated that these biases can
spuriously change the temporal climate evolution of transient paleoclimate simulations.
[35] For the comparison with paleoproxies and their
seasonal interpretation, the precise season definition is less
important because proxies with sharp seasonal response
functions are very rare in nature. Most proxies represent
annual mean quantities or a weighted average of the
seasons. Model comparisons with ice core records or marine
sediments records therefore will usually require seasonally
weighted annual means. Furthermore, the natural tendency
of the ocean to reduce the annual cycle reduces the bias in
SSTs. Comparisons between seasonal model output and
tropical marine proxies is therefore not limited by the
definition of seasons.
[36] Isotopic d 18O records from speleothems represent
changes in the amplitude of the seasonal precipitation cycle
in tropical and subtropical regions. Their distinctive response function makes it necessary to use appropriate
indices for comparison with models. We recommend the
use of fixed angular seasons for these type of proxies. Our
model simulation reproduces the strong precessional cycles
that are recorded in the speleothem records in Asia and
South Brazil. The antiphasing between both hemispheres is
a robust feature and further supports Kutzbach’s paleomonsoon theory.
[37] We note that the problem of the season definition has
already been addressed during the PMIP time slice experiments (PMIP newsletter number 1, 1993, available online at
http://pmip.lsce.ipsl.fr/newsletters/newsletter01.html). Our
results systematically quantify the associated differences
between the two definitions of seasons. These estimates
provide guidelines for the interpretation of upcoming transient paleoclimate model simulations and for forthcoming
proxy-model intercomparisons.
Appendix A
[38] Let xi(t) represent a climate variable (e.g., temperature) for a given day i in the paleoyear t (e.g., 11,000 B.P.).
With the 360 days put into a vector x(t), the four seasonal
averages can be expressed as a matrix operation that
projects the daily data x(t) onto seasonal means y(t):
ya ðtÞ ¼ Aa ðtÞxðtÞ;
ðA1Þ
yc ðtÞ ¼ Ac xðtÞ:
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ðA2Þ
[39] A(t) is the averaging matrix operator. The subscript a
(c) denotes the fixed angular (fixed calendar) seasons. Note
that Aa(t) depends on the eccentricity and phase of the
precession and hence varies on orbital timescales. The
vector x(t) can be decomposed into
xðtÞ þ x0 ðtÞ;
xðtÞ ¼ x0 þ ~
ðA3Þ
~(t)
with x0 denoting the preindustrial annual cycle, x
denoting the orbitally driven anomalous annual cycle, and
x0(t) representing interannual anomalies. The contribution
of the latter term mainly reflects interannual variability.
Note that random-like weather fluctuations also fall into this
category. Since the decorrelation time of weather variability
is generally less than the length of the seasons, the seasonal
averaging eliminates most of the random fluctuations. The
interannual fluctuations can be reduced by averaging the
resulting seasons over several years with equivalent orbital
configurations. Therefore, if the interannual anomalies x0(t)
are neglected, the difference between the fixed calendar
and fixed angular seasonal averages contains two components. With the annual cycle expressed as a preindustrial
mean and its anomalies, the differences between the
calendar day and angular seasons become
xðtÞ;
yc ðtÞ ya ðtÞ ¼ ½Ac Aa ðtÞx0 þ ½Ac Aa ðtÞ~
ðA4Þ
or equivalently
~
dðtÞ ¼ d0 ðtÞ þ dðtÞ:
ðA5Þ
[40] The first term on the right-hand side d0(t) captures
the effect of the calendar versus angular season definition
(and its modulation through time) on the preindustrial
annual cycle (see also Figure 3 for an illustration) The
~
second term d(t)
is a projection of the anomalous annual
cycle on the different days in the averaging operation.
Provided that the preindustrial mean annual cycle x0 is
available, one can estimate the difference d0(t) and partly
correct calendar-based seasonal averages. We used the
preindustrial annual cycle x0 to estimate the term d0(t).
[41] Acknowledgments. The authors are grateful to the editors for
their helpful comments. The constructive criticism of David Pollard and an
anonymous reviewer significantly improved the manuscript. We thank
Carolyn A. Dykoski and colleagues, Yongjin Wang and colleagues, and
Francisco W. Cruz Jr. and colleagues for providing their data through the
IGBP PAGES/World Data Center for Paleoclimatology (NOAA/NCDC
Paleoclimatology Program, Boulder, Colorado, USA). The authors acknowledge Niklas Schneider for stimulating discussions. This research
project was supported by the Japan Agency for Marine-Earth Science and
Technology (JAMSTEC) through its sponsorship of the International
Pacific Research Center. This is International Pacific Research Center
contribution number 513 and School of Ocean and Earth Science and
Technology contribution number 7339.
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