On the definition of seasons in paleoclimate ... - Wiley Online Library

PALEOCEANOGRAPHY, VOL. 23, PA2221, doi:10.1029/2007PA001461, 2008

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

[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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TIMM ET AL.: ON THE DEFINITION OF PALEOSEASONS

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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 [Indermu¨hle 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 ðtÞ x0 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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A. Abe-Ouchi, Center for Climate Research, University of Tokyo, Kashiwa 277-8568, Japan. F. Saito and T. Segawa, Frontier Research Center for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan. O. Timm and A. Timmermann, International Pacific Research Center, SOEST, University of Hawai’i at Manoa, POST Building 401, Honolulu, HI 96822, USA. ([email protected])