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    Change in annual-mean 2-m air temperature (°C) in the (a) Lo-Hi obliquity, (b) WS-SS perihelion, (c) HalfCO2, and (d) IceSheets fingerprint experiments. Note the differences in scale. Anomalies that are not significant at the 0.05 level, according to a two-tailed t test, are hatched.

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    As in Fig. 1, but for annual-mean precipitation (mm day−1). Note the differences in scale.

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    Longitude of perihelion that produces the maximum annual-mean precipitation, determined by computing a first harmonic of the precipitation values of the four idealized precession simulations. At each point, the direction of the vector indicates the estimated longitude of perihelion of maximum precipitation, which can be interpreted with the vector key. The length of the vector (and the shading) indicating the relative amplitude of the harmonic.

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    Change in annual-mean 2m air temperature (°C) for 6ka-preind in the (a) snapshot experiment and (b) reconstruction. The reconstruction may be separated into its two components: change in annual-mean 2-m air temperature due to (c) obliquity and (d) precession. (e) The reconstruction-snapshot mismatch, showing the anomaly for (b)–(a).

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    As in Fig. 4, but for annual-mean precipitation (mm day−1).

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    Scatterplots of snapshot (x axis) vs reconstructed (y axis) 2-m air temperature anomalies (°C) for five different latitude bands in the (left) 6ka-preind and (right) LGM-preind experiments. Black Xs show monthly anomalies while red Xs show annual means. (top to bottom) The latitude bands correspond to the Arctic, NH midlatitudes, tropics, SH midlatitudes, and the Antarctic. The blue line marks the 1:1 ratio.

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    Scatterplots of snapshot (x axis) vs reconstructed (y axis) precipitation anomalies (mm day−1) for all grid points in the (left) 6ka-preind and (right) LGM-preind experiments. Black Xs show monthly anomalies while red Xs show annual means. The blue line marks the 1:1 ratio.

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    Change in annual-mean 2-m air temperature (°C) for LGM-preind in the (a) snapshot experiment and (b) reconstruction. The reconstruction may be separated into its components, two of which are shown: annual-mean 2-m air temperature anomalies due to changes in (c) greenhouse gases and (d) ice sheets. Obliquity and precession also affect temperature, but those changes are small in comparison. (e) The reconstruction-snapshot mismatch, showing the anomaly for (b)–(a).

  • View in gallery

    As in Fig. 8, but for annual-mean precipitation (mm day−1).

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    Change in annual-mean near-surface air temperature anomalies (°C) in CMIP5 ensembles for (a) 6ka-preind (eight models) and (b) LGM-preind (five models). Anomalies that are not significant among the CMIP5 models at the 0.05 level, according to a paired two-tailed t test, are hatched.

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    As in Fig. 10, but for annual-mean precipitation (mm day−1).

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    Change in annual-mean AMOC (Sv) for the (a) 6ka-preind snapshot, (b) 6ka-preind reconstruction, (c) LGM-preind snapshot, and (d) LGM-preind reconstruction. Note the differences in scale. For 6ka-preind, changes in maximum overturning are 1.13 Sv for the snapshot and −0.06 Sv for the reconstruction (with −0.33 Sv for the obliquity component and 0.27 Sv for the precession component). For LGM-preind, changes in maximum overturning are 7.01 Sv for the snapshot and 10.01 Sv for the reconstruction (with −1.93 Sv for greenhouse gases, 11.11 Sv for ice sheets, 0.25 Sv for obliquity, and 0.00 Sv for precession). Stated changes in maximum overturning do not correspond directly to changes shown in the figure because locations of maximum overturning do not need to be coincident. Changes in maximum overturning in each component do not necessarily sum to the change in the reconstruction for the same reason.

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    Change in temperature (°C) determined from proxy records compared to time series reconstructions at those locations. (a) SST from Mg/Ca in ocean sediment core TR163-19 [eastern equatorial Pacific; Lea (2004)], (b) SST from Mg/Ca in ocean sediment core ODP806b [western equatorial Pacific; Lea et al. (2000)], (c) air temperature from deuterium in Vostok ice core (Petit et al. 1999), and (d) surface temperature from GISP2 ice core (Alley 2000). The proxy record (thick black) is compared to a linear time series reconstruction (dotted blue). The linear reconstruction is the sum of components from obliquity (red), precession (orange), greenhouse gases (green), and ice sheets (gray), showing temperature difference relative to an idealized zero eccentricity state. While the reconstruction was calculated with a 1-ka time resolution, it is here regridded to the time axes of the proxy records. The mean temperature difference between the proxy record and the reconstruction has been removed from each proxy record, resulting in the proxies not having values of 0 at the present.

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Using Single-Forcing GCM Simulations to Reconstruct and Interpret Quaternary Climate Change

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  • 1 Institute for Geophysics, The University of Texas at Austin, Austin, Texas
  • 2 Department of Environmental Sciences, and Institute of Earth, Ocean and Atmospheric Sciences, Rutgers, The State University of New Jersey, New Brunswick, New Jersey
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Abstract

The long-term climate variations of the Quaternary were primarily influenced by concurrent changes in Earth’s orbit, greenhouse gases, and ice sheets. However, because climate changes over the coming century will largely be driven by changes in greenhouse gases alone, it is important to better understand the separate contributions of each of these forcings in the past. To investigate this, idealized equilibrium simulations are conducted in which the climate is driven by separate changes in obliquity, precession, CO2, and ice sheets. To test the linearity of past climate change, anomalies from these single-forcing experiments are scaled and summed to compute linear reconstructions of past climate, which are then compared to mid-Holocene and last glacial maximum (LGM) snapshot simulations, where all forcings are applied together, as well as proxy climate records. This comparison shows that much of the climate response may be approximated as a linear response to forcings, while some features, such as modeled changes in sea ice and Atlantic meridional overturning circulation (AMOC), appear to be heavily influenced by nonlinearities. In regions where the linear reconstructions replicate the full-forcing experiments well, this analysis can help identify how each forcing contributes to the climate response. Monsoons at the mid-Holocene respond strongly to precession, while LGM monsoons are heavily influenced by the altered greenhouse gases and ice sheets. Contrary to previous studies, ice sheets produce pronounced tropical cooling at the LGM. Compared to proxy temperature records, the linear reconstructions replicate long-term changes well and also show which climate variations are not easily explained as direct responses to long-term forcings.

Corresponding author address: Michael P. Erb, Institute for Geophysics, The University of Texas at Austin, J. J. Pickle Research Campus, Bldg. 196, 10100 Burnet Rd., Austin, TX 78758. E-mail: merb@ig.utexas.edu

Abstract

The long-term climate variations of the Quaternary were primarily influenced by concurrent changes in Earth’s orbit, greenhouse gases, and ice sheets. However, because climate changes over the coming century will largely be driven by changes in greenhouse gases alone, it is important to better understand the separate contributions of each of these forcings in the past. To investigate this, idealized equilibrium simulations are conducted in which the climate is driven by separate changes in obliquity, precession, CO2, and ice sheets. To test the linearity of past climate change, anomalies from these single-forcing experiments are scaled and summed to compute linear reconstructions of past climate, which are then compared to mid-Holocene and last glacial maximum (LGM) snapshot simulations, where all forcings are applied together, as well as proxy climate records. This comparison shows that much of the climate response may be approximated as a linear response to forcings, while some features, such as modeled changes in sea ice and Atlantic meridional overturning circulation (AMOC), appear to be heavily influenced by nonlinearities. In regions where the linear reconstructions replicate the full-forcing experiments well, this analysis can help identify how each forcing contributes to the climate response. Monsoons at the mid-Holocene respond strongly to precession, while LGM monsoons are heavily influenced by the altered greenhouse gases and ice sheets. Contrary to previous studies, ice sheets produce pronounced tropical cooling at the LGM. Compared to proxy temperature records, the linear reconstructions replicate long-term changes well and also show which climate variations are not easily explained as direct responses to long-term forcings.

Corresponding author address: Michael P. Erb, Institute for Geophysics, The University of Texas at Austin, J. J. Pickle Research Campus, Bldg. 196, 10100 Burnet Rd., Austin, TX 78758. E-mail: merb@ig.utexas.edu

1. Introduction

Over the glacial cycles of the past several million years, slow variations in Earth’s orbit have initiated large climate shifts through the growth and decay of ice sheets and changes in greenhouse gas concentrations (Hays et al. 1976). Together, these three factors—changes in orbit, ice sheets, and greenhouse gases—have driven much of the long time-scale climate variations of the Quaternary. By forcing the climate system with combinations of these factors, general circulation models (GCMs) can be used to further our understanding of the climate system.

One method of modeling past climate is with “snapshot” simulations, in which all forcings are applied together. While these more realistic simulations are useful for comparison with proxy data, it is difficult to determine the individual contributions of each forcing to the total climate response. For example, colder temperatures at the last glacial maximum (LGM) are largely due to lowered CO2 and increased ice sheet extent, but the relative contribution of each factor to the total response is difficult to determine from a single experiment. The question of linearity is also difficult to answer: is the total climate response primarily a linear combination of responses to individual forcings, or is the climate response more dependent on multiple forcings acting in unison? Because climate change over the coming century will be driven primarily by a single forcing (i.e., greenhouse gases), it is important to understand the individual contributions of forcings in causing Quaternary climate change.

Several past studies have focused on isolating the individual contributions of forcings in different ways. Orbital forcings, for example, have been investigated both by simulating climate under selected orbital setups (e.g., Phillipps and Held 1994) and by forcing climate with the transient orbital configuration of the past many thousand years (e.g., Jackson and Broccoli 2003; Kutzbach et al. 2008). To separate other forcings, studies have conducted multiple series of snapshot simulations (Felzer et al. 1998; Singarayer and Valdes 2010) or accelerated and nonaccelerated transient simulations (Timmermann et al. 2009; He et al. 2013) with different combinations of orbital, ice sheet, Atlantic meridional overturning circulation (AMOC), and greenhouse gas forcings.

Additional research has investigated the degree of linearity in the climate response to these forcings. While nonlinearities are certainly present in the climate system, several studies have suggested that a linear approximation can account for much of the climate’s response to combined forcings (Felzer et al. 1998; Jackson and Broccoli 2003). Using a model with a mixed layer ocean, Jackson and Broccoli (2003) find that their transient, orbitally forced simulation can be well represented as a linear combination of separate obliquity and precession responses.

A method of investigating linearity in more detail is the factor separation approach, in which climate simulations are driven by separate forcings as well as every combination of forcings for a given time period (Stein and Alpert 1993; Henrot et al. 2009; Yin and Berger 2010, 2012). While effective, a pure factor separation approach requires many simulations to separate out the interactions between multiple forcings, which can become computationally expensive. Because of this, many factor separation studies often employ an Earth system model of intermediate complexity (EMIC) or other reduced-order model rather than a coupled GCM, possibly missing important aspects of the climate response.

Araya-Melo et al. (2015) employ a different experimental design to investigate linearity. By running a large number of simulations with different sets of forcings, optimally separated in parameter space, they construct an “emulator” that can estimate climate change under any set of forcings. For specific variables related to the Indian monsoon, Araya-Melo et al. find that the responses to CO2 and obliquity forcings are largely linear, while the responses to precession and ice are less so.

The present research uses atmosphere–ocean GCM simulations to further investigate the individual contributions of forcings to past climate change, with a focus on exploring the linearity of the climate system under multiple forcings. Idealized equilibrium simulations are conducted in which the climate is separately forced with changes in obliquity, precession, CO2, and ice sheets. To evaluate nonlinearities in the climate response to multiple forcings, a linear reconstruction methodology is employed in which anomalies from these single-forcing experiments are scaled and combined to approximate past climate change. Comparisons of linear reconstructions against mid-Holocene (6 ka) and LGM snapshot experiments, in which all forcings are applied together, reveals the approximate contribution of each forcing to the total response as well as the potential influence of nonlinearities. Comparison of time series reconstructions to proxy records evaluates the degree to which the single-forcing experiments are consistent with past climate change.

An advantage of this experimental design over a pure factor separation experiment is that one set of simulations may be scaled and used to study any time period. Additionally, the relatively small number of simulations makes it more feasible to employ a coupled atmosphere–ocean GCM. Compared to the emulator method of Araya-Melo et al. (2015), the methodology employed here is much less computationally expensive. A trade-off is that it is more difficult to isolate and understand the specific nonlinearities in the climate response. With this limitation in mind, two questions are explored: how do individual Quaternary forcings affect the climate system, and to what degree can past climate change be regarded as a linear combination of these responses?

Section 2 of this paper lays out the experimental design. Section 3 examines the climate response in the single-forcing experiments, laying the groundwork for interpreting the linear reconstructions later on. In sections 4 and 5, linear reconstructions of mid-Holocene and LGM climate anomalies are compared to snapshot experiments to examine the temperature and precipitation responses under individual versus combined forcings. Section 6 offers some additional discussion about the snapshot reconstructions, as well as some of the promise and shortcomings of this methodology. In section 7, time series reconstructions are compared with proxy records to evaluate how well the modeled climate responses are supported by the paleo record. The paper’s conclusions are stated in section 8.

2. Experimental design

This research uses the Geophysical Fluid Dynamics Laboratory (GFDL) Climate Model 2.1 (CM2.1), a coupled GCM with atmosphere, ocean, land, and sea ice components (Delworth et al. 2006). It has horizontal resolution of 2° by 2.5° in the atmosphere, with 24 vertical levels, and horizontal resolution of 1° by 1° in the ocean, becoming finer in the tropics, with 50 vertical levels. Reichler and Kim (2008) found that CM2.1 produced the best modern climate and one of the best preindustrial climates in a comparison with 21 other models from phase 3 of the Coupled Model Intercomparison Project (CMIP3).

The GFDL CM2.1 is used to run idealized equilibrium simulations that isolate the climate response to changes in obliquity, precession, CO2, and ice sheets (Table 1). For obliquity, simulations use values of the low (22.079°) and high (24.480°) extremes of the past 600 ka (Berger and Loutre 1991). For precession, four simulations set the date of Earth’s perihelion to the Northern Hemisphere (NH) autumnal equinox, winter solstice, vernal equinox, and summer solstice, with eccentricity increased to its maximum value of the past 600 ka to amplify the response. An additional simulation has an eccentricity of zero, indicating a perfectly circular orbit and therefore no perihelion, which is a useful reference. For CO2, a simulation is run with half the preindustrial value of CO2 (143 ppm). For ice sheets, the climate is forced with the ice sheets and coastlines of the LGM (ICE-5G from Peltier 2004). All forcings not mentioned are set to preindustrial levels. Single-forcing equilibrium simulations are run for at least 600 years, and all output is analyzed as 100-yr climatologies. Because the deep ocean may not yet be fully equilibrated to the forcings in these simulations, analysis is generally confined to the atmosphere and upper ocean.

Table 1.

Values of orbital parameters, CO2, and ice sheets used in the three snapshot simulations and nine idealized simulations. Cells marked with “—” have values identical to preindustrial. Precession simulations are named according to the date of perihelion, with perihelion occurring at the NH autumnal equinox (AE), winter solstice (WS), vernal equinox (VE), and summer solstice (SS). Values of CH4 and N2O are identical across all simulations except LGM, where they are lower.

Table 1.

For monthly output, a calendar adjustment has been made. Because changing the date of perihelion can alter the timing of equinoxes and solstices according to Kepler’s second law (Joussaume and Braconnot 1997), monthly anomalies on standard fixed-day calendars are difficult to interpret. As a solution, monthly output in all simulations is converted to a common fixed-angular calendar, in which “months” are defined as 30° arcs of orbit, using the method described in Pollard and Reusch (2002).

The influence of individual forcings on the climate system can be examined in these simulations directly. However, to determine the relative influence of these forcings in the past, and to estimate the effect of nonlinearities, linear reconstructions of past climate anomalies are computed. To do this, climate anomalies from the single-forcing experiments are scaled by past forcings and summed together. As a simple example, the temperature anomaly due to a change in obliquity can be approximated with the following equation:
eq1
where is the obliquity at a specified time; is the preindustrial obliquity value; and are the obliquity values from the high and low obliquity simulations, respectively; and and are the temperatures from the high and low obliquity simulations, respectively. This calculation scales the obliquity climate anomaly, computed as the difference between the high and low obliquity simulations, by the desired relative change in that parameter. The contribution of other forcings can be added in a similar manner, with the effect of precession calculated from the four precession simulations by making a sinusoidal fit to the model results then scaling by eccentricity; the effect of CO2 change scaled by the radiative forcing of CO2; and the effect of ice sheets scaled according to past sea level change (as an analog for total ice sheet volume). The effect of CH4 change is also included by scaling the climate response to CO2 by the relative radiative forcing of CH4, which avoids the need for a dedicated CH4 simulation. The treatment of CH4 as CO2 equivalent forcing may not be ideal (Sugi and Yoshimura 2004), but whatever biases this approximation introduces should be small. Full reconstruction equations are given in the appendix.

Using this method, linear climate reconstructions are first computed for the preindustrial, mid-Holocene, and LGM. These reconstructed climate anomalies are compared to anomalies between preindustrial, mid-Holocene, and LGM snapshot simulations, where all forcings are applied together.

Time series linear reconstructions are calculated in the same way, but are computed every 1 ka using time-varying records of orbital parameters (Berger and Loutre 1991), CO2 and CH4 (Petit et al. 1999), and relative sea level (Rohling et al. 2009, 2010). It should be noted that, while changes in sea level is a good analog for total ice sheet volume, the climate is also affected by the surface area of ice sheets, which can evolve differently with time. While this shortcoming may affect the linear time series reconstructions in section 7, this methodology was chosen because of the availability of sea level records through time. Additionally, the use of a simple linear interpolation between the effects of preindustrial and LGM ice sheets ignores potential nonlinearities in the climate’s response to changing ice sheets (Zhang et al. 2014; Lee et al. 2015; Lu et al. 2015). While this should not affect the 6-ka and LGM reconstructions, it should be kept in mind when interpreting the time series reconstructions. Finally, to account for age model differences in the various records, most records are temporally aligned with the LR04 stack using matching software (Lisiecki and Raymo 2005; Lisiecki and Lisiecki 2002).

The linear climate reconstructions assume two things: that climate responses to individual forcings scale linearly with the forcings and that there are no interactions between the responses to multiple forcings. To at least some extent, these assumptions are not true of the real climate system, but the full importance of these nonlinearities is unclear. Comparison of the reconstructions with snapshot experiments and proxy records tests the importance of such processes in CM2.1’s climate response and estimates the relative importance of each past forcing in producing climate change. Comparison of 6-ka and LGM experiments from CM2.1 and phase 5 of the Coupled Model Intercomparison Project (CMIP5) models help put CM2.1 results in perspective with those of the broader modeling community.

Some features of these obliquity and precession experiments have been described in previous papers, which focus on the role of feedbacks in the orbital experiments (Mantsis et al. 2011; Erb et al. 2013), atmospheric circulation changes in response to altered obliquity (Mantsis et al. 2014), and the effect of precession on equatorial Pacific seasonality (Erb et al. 2015). The response of midlatitude anticyclones to precession forcing is examined in a similar set of precession simulations (Mantsis et al. 2013). The half CO2 and ice sheets simulations have not been previously analyzed.

3. Climate response fingerprints

Before looking at the linear reconstructions of past climate, it is useful to evaluate the climate response to each forcing alone. The responses are analyzed as a lowering of obliquity (the Lo-Hi obliquity experiment), a change in the timing of perihelion from the NH summer solstice to winter solstice (WS-SS perihelion), a halving of CO2 (HalfCO2), and the presence of LGM ice sheets and sea level (IceSheets). Because these simulations isolate distinctive responses to each type of forcing, they are here referred to as “fingerprint” simulations. Additional precession simulations are given less attention for the sake of brevity.

The Lo-Hi obliquity experiment is characterized by a reduction of axial tilt from ~24.5° to ~22°, which reduces insolation during high-latitude summer in both hemispheres and slightly increases insolation at the equator and in midlatitude winter. Changes in obliquity (and longitude of perihelion) do not increase or decrease annual, global mean insolation, but do affect its seasonal and latitudinal distribution. Despite this, the lowered obliquity cools high latitudes more than it warms low latitudes (Fig. 1a), decreasing global mean temperature by 0.5°C due to the influence of feedbacks (Mantsis et al. 2011; Erb et al. 2013). The decreased interhemispheric temperature contrasts also influence the seasonal components of the Hadley circulation, which consist of a strong winter hemisphere cell and a weaker summer hemisphere cell during “solsticial” seasons (Dima and Wallace 2003). The winter hemisphere Hadley cell weakens and the summer hemisphere Hadley cell strengthens, resulting in an ITCZ that does not shift as far north or south during the seasonal cycle, as well as a reduction in cross equatorial heat transport (Mantsis et al. 2014). Mean precipitation is generally increased along the equator and reduced near ~10°–40° in both hemispheres (Fig. 2a).

Fig. 1.
Fig. 1.

Change in annual-mean 2-m air temperature (°C) in the (a) Lo-Hi obliquity, (b) WS-SS perihelion, (c) HalfCO2, and (d) IceSheets fingerprint experiments. Note the differences in scale. Anomalies that are not significant at the 0.05 level, according to a two-tailed t test, are hatched.

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

Fig. 2.
Fig. 2.

As in Fig. 1, but for annual-mean precipitation (mm day−1). Note the differences in scale.

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

In the WS-SS perihelion experiment, perihelion is moved from the NH summer solstice to the NH winter solstice, weakening the seasonal insolation cycle in the NH and strengthening it in the Southern Hemisphere (SH). Monsoons weaken in the NH and strengthen in the SH, influencing both the precipitation and temperature in monsoon regions. Over northern Africa and India, for example, less-cloudy wet seasons allow additional sunlight to reach the ground, raising temperatures. To estimate the phase of perihelion that results in the strongest monsoons for each region, a first harmonic of annual-mean precipitation is computed using all four precession simulations (Fig. 3). The first harmonic calculation works by fitting a sinusoidal curve to the four data points at each location using a least squares fit, and is done so that the magnitude and timing of the maximum values can approximated. This analysis suggests that the strongest precipitation occurs when perihelion is a little later in the year than the summer solstice. Because annual-mean precipitation in monsoon regions is largely driven by monsoonal precipitation, it is curious why maximum precipitation is not coincident with the largest seasonal insolation cycle (longitude of perihelion at 270° and 90° for the NH and SH, respectively). The first harmonic calculation is based on equilibrium simulations, so time lags are not present. Conducting this calculation for summer precipitation alone [June–August (JJA) and December–February (DJF)] gives a similar result: the strongest monsoons are calculated to occur when perihelion is a few days to a few weeks after the summer solstice in each hemisphere. On average, these perihelion dates are a few weeks later than those suggested by Kutzbach et al. (2008), which used a lower-resolution transient simulation. For comparison, the phasing of maximum summer temperatures in these simulations matches well with the findings of Kutzbach et al. (2008), with maximum JJA temperatures in the NH coincident with maximum June insolation over land but offset by ~40° over the ocean (not shown). These results suggest that the phasing of monsoonal precipitation described by Kutzbach may be more model dependent than the phasing of temperatures. The result that the northern African monsoon responds to a later phase of precession than the Indian monsoon in CM2.1 is consistent with Marzin and Braconnot (2009), who suggest that the northern African monsoon is more sensitive to insolation in the late, rather than early or middle, summer.

Fig. 3.
Fig. 3.

Longitude of perihelion that produces the maximum annual-mean precipitation, determined by computing a first harmonic of the precipitation values of the four idealized precession simulations. At each point, the direction of the vector indicates the estimated longitude of perihelion of maximum precipitation, which can be interpreted with the vector key. The length of the vector (and the shading) indicating the relative amplitude of the harmonic.

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

In the HalfCO2 experiment, reduced CO2 causes a widespread cooling, with a global mean 2-m air temperature change of −4.0°C (Fig. 1c). Lower-latitude continents tend to cool slightly more than nearby oceans, generally consistent with the suggestion that greater changes in evaporation over the oceans offset some of the temperature change there (Sutton et al. 2007). Accompanying the colder temperatures, precipitation is generally reduced, with the largest negative anomalies along the equator, especially over the western equatorial Pacific (Fig. 2c). This is consistent with the precipitation response to global warming, which shows a general wet-get-wetter pattern driven by thermodynamic and dynamic processes (Bony et al. 2013).

The IceSheets experiment is also dominated by cooling, but the regional pattern of cooling is much different than in the HalfCO2 experiment. The largest changes occur over the new or expanded ice sheets in North America, Europe, and Antarctica. Factor separation studies have found that ice sheets primarily cool climate through their low albedo, with increased elevation having a smaller effect (Henrot et al. 2009; Yin et al. 2009). Temperature anomalies are smaller away from the ice sheets, but the widespread cooling in this experiment, especially in the SH, differs from past ice sheet experiments (Broccoli and Manabe 1987; Henrot et al. 2009; Yin et al. 2009), which show areas of warming in the SH or ocean areas. Those studies used EMICs or had simple oceans, however, so the current results suggest that widespread cooling may be a more realistic response to expanded NH and Antarctic ice sheets. This cooling is aided by the radiative effects of increased low clouds and reduced water vapor. The degree of cooling in CM2.1 is also well replicated in a CESM1(CAM5) simulation forced with LGM ice sheets alone (P. DiNezio 2015, personal communication). The tropics cool by 1.8°C in CM2.1 and 1.5°C in CESM in these ice sheet experiments. The relative agreement between these two AOGCMs suggests a need to reevaluate the effect of ice sheet forcing on tropical and SH temperatures. Regarding precipitation, much of the ITCZ shifts south in response to substantial NH cooling, consistent with the southward ITCZ shift in other NH cooling experiments (Broccoli et al. 2006). However, because of the model’s double ITCZ bias, which is common to many GCMs (Wittenberg et al. 2006; Lin 2007), the particulars of the response should be taken with some caution. Both the HalfCO2 and IceSheets experiments cool the global mean climate, but produce very different patterns of temperature and precipitation change.

Following the method outlined in the experimental design, these idealized fingerprint simulations are scaled and combined to make linear climate reconstructions at preindustrial, 6 ka, and LGM, as well as time series at particular locations. For the 6-ka minus preindustrial (6ka-preind) experiment, comparing the reconstruction anomalies with modeled snapshot anomalies explores the effects of orbital forcing, since greenhouse gases and ice sheets do not change between the 6-ka and preindustrial simulations. The LGM minus preindustrial (LGM-preind) experiment also has orbital changes, but analysis of that reconstruction focuses on the effects of greenhouse gases and ice sheets, since direct orbital effects are small in comparison. In areas where a linear reconstruction does a good job approximating the full climate change, the components of the reconstruction suggest the relative impacts of each forcing. Time-varying reconstructions are analyzed in a later section.

4. The mid-Holocene reconstruction

Proxy records suggest that mid-Holocene climate was slightly warmer than preindustrial, with much of this warm anomaly in the NH (Marcott et al. 2013). Because the large ice sheets of the previous glacial had melted closer to preindustrial levels and greenhouse gas levels had risen, differences in orbit, with possible contributions from solar output and volcanic activity, were the likely cause of anomalies (Wanner et al. 2008). In the mid-Holocene simulation, no solar or volcanic anomalies are applied, so the altered orbit is the sole driver of change. Obliquity was higher at the mid-Holocene than preindustrial (~24° vs ~23.5°), eccentricity was slightly higher, and perihelion occurred about four months earlier in the year: near the NH autumnal equinox rather than in early January. In addition to affecting the seasonal insolation cycle, this reduces annual-mean insolation by nearly 1 W m−2 at the equator and increases it by ~4.6 W m−2 at the poles.

In the mid-Holocene snapshot experiment, annual-mean temperature warms over the NH mid- and high latitudes, parts of Antarctica, and some SH continental areas, while cooling dominates the SH ocean regions and NH monsoon regions (Fig. 4a). The change in orbit increases the seasonal insolation cycle in the NH and decreases it in the SH. In response, precipitation is increased over NH monsoon regions and decreased in SH monsoon regions during each hemisphere’s summer and fall, with corresponding effects on annual-mean precipitation (Fig. 5a). Analogous to the precession experiment, strengthened NH monsoons facilitate cooling over northern Africa and India (as in Braconnot et al. 2007a), while weakened SH monsoons lead to warming over SH continents.

Fig. 4.
Fig. 4.

Change in annual-mean 2m air temperature (°C) for 6ka-preind in the (a) snapshot experiment and (b) reconstruction. The reconstruction may be separated into its two components: change in annual-mean 2-m air temperature due to (c) obliquity and (d) precession. (e) The reconstruction-snapshot mismatch, showing the anomaly for (b)–(a).

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

Fig. 5.
Fig. 5.

As in Fig. 4, but for annual-mean precipitation (mm day−1).

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

This stronger NH/weaker SH monsoon response, and other aspects of the mid-Holocene climate, is generally consistent with previous modeling results. Early work showed strengthened NH monsoons in response to the larger NH insolation cycle of 9 ka (Kutzbach 1981; Kutzbach and Otto-Bliesner 1982; Kutzbach and Guetter 1986). More recently, Zhao and Harrison (2012) analyzed results from Paleoclimate Modelling Intercomparison Project (PMIP) 1 and 2 and concluded that changes in summer insolation at the mid-Holocene strengthen NH monsoons and weaken SH monsoons. The comparison of atmosphere-only PMIP1 simulations with coupled PMIP2 simulations suggests that ocean feedbacks help strengthen NH monsoons but limit the weakening of SH monsoons, similar to the results of earlier research (Liu et al. 2004).

Some proxy records also support these monsoonal changes. Speleothem δ18O records from different regions suggest stronger mid-Holocene monsoons in East Asia, India, and the eastern Mediterranean and a weaker monsoon in South America, probably driven by precession (Cheng et al. 2012; Wang et al. 2008). A sediment record from the Pretoria Saltpan suggests that the southern African monsoon was also weaker (Partridge et al. 1997). Pollen data show wetter conditions in northern Africa and India, but the pollen data differ from the PMIP results in parts of southern Africa, where they show wetter conditions (Bartlein et al. 2011; Zhao and Harrison 2012). This disagreement suggests a need to better understand past monsoonal changes and the mechanisms behind them.

The linear reconstruction captures many aspects of the climate response, showing similar annual-mean temperature changes for the NH and parts of the tropics, including the large temperature and precipitation changes over monsoonal regions (Figs. 4b and 5b). A pronounced mismatch, however, occurs over the Southern Ocean, which cools in the snapshot experiment but warms in the reconstruction. The reason for this mismatch might have to do with sea ice, as differences are also apparent in the Bering Sea. Among different models, sea ice response can vary greatly even when forcing is the same, such as with PMIP2 LGM simulations (Braconnot et al. 2007b), suggesting that the sea ice response may be particularly sensitive to the details of the simulation.

In regions where mismatches are less pronounced, the obliquity and precession components of the reconstruction can be used to better understand changes. Increased obliquity causes warming in the mid- and high latitudes and a small amount of cooling in the tropics (Fig. 4c). Precession is responsible for the majority of the precipitation changes over both land and ocean, providing the bulk of the stronger NH/weaker SH monsoon response. As described in Zhao and Harrison (2012), increased boreal summer insolation warms the continents and creates anomalous low pressure over land, enhancing onshore flow and increasing precipitation in NH monsoon regions. A similar, but opposite, response occurs over SH continents during austral summer. In comparison, obliquity has a smaller effect on mid-Holocene precipitation: increased cross-equatorial insolation gradients during the year strengthen the winter Hadley cells, shifting the ITCZ farther north and south during its seasonal cycle. However, precipitation changes due to precession are generally several times larger than those due to obliquity.

Changes in summer precipitation (JJA in NH, DJF in SH) for the mid-Holocene experiments are given for six monsoon regions in Table 2. In each region, the precession component of the reconstruction accounts for essentially the entire change, with obliquity having comparatively small effects on monsoonal strength. Because of the skill of the reconstruction in capturing monsoonal changes, it seems plausible to suggest that, at least in this model, monsoons can largely be regarded as a linear response to forcings, with precession having the dominant influence.

Table 2.

Change in summer precipitation (JJA in NH, DJF in SH) for six monsoon regions for 6ka-preind (mm day−1). Values are calculated for the snapshot experiment, reconstruction, and the obliquity and precession components of the reconstruction. The monsoon regions are defined as land within the following areas: North American (0°–40°N, 130°–60°W), northern African (0°–40°N, 20°W–45°E), Asian (0°–40°N, 60°–150°E), South American (40°–0°S, 90°–30°W), southern African (40°S–0°, 0°–60°E), and Australian (40°S–0°, 100°–160°E).

Table 2.

Over the ocean, precipitation changes are harder to interpret (Fig. 5). In the Atlantic, the increased NH summer insolation shifts additional precipitation over northern Africa at the expense of the northern equatorial Atlantic. According to Braconnot et al. (2007a), warming in the NH Atlantic strengthens northward flow and shifts the ITCZ farther north. In the Indian Ocean, stronger trades develop in NH summer and fall and shift precipitation farther west, so that a wet/dry dipole develops along the equator. This Indian Ocean response appears to be driven primarily by precession, but a weaker pattern develops in response to the increased obliquity.

As a general test of the reconstructions, temperature and precipitation anomalies are compared between the snapshots and reconstructions (Figs. 6 and 7). For temperature, the scatterplots are separated into five latitudinal bands corresponding to the Arctic, NH midlatitudes, tropics, SH midlatitudes, and the Antarctic. The largest precipitation anomalies occur at low latitudes, so no latitudinal separation is made for precipitation. In addition to annual-mean anomalies, the scatterplots also display monthly anomalies, to show the degree to which seasonal changes are captured by the reconstructions.

Fig. 6.
Fig. 6.

Scatterplots of snapshot (x axis) vs reconstructed (y axis) 2-m air temperature anomalies (°C) for five different latitude bands in the (left) 6ka-preind and (right) LGM-preind experiments. Black Xs show monthly anomalies while red Xs show annual means. (top to bottom) The latitude bands correspond to the Arctic, NH midlatitudes, tropics, SH midlatitudes, and the Antarctic. The blue line marks the 1:1 ratio.

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

Fig. 7.
Fig. 7.

Scatterplots of snapshot (x axis) vs reconstructed (y axis) precipitation anomalies (mm day−1) for all grid points in the (left) 6ka-preind and (right) LGM-preind experiments. Black Xs show monthly anomalies while red Xs show annual means. The blue line marks the 1:1 ratio.

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

Both temperature and precipitation anomalies show strong correlations in the scatterplots. In the NH and tropics, reconstructed mid-Holocene temperature matches the snapshot simulations well, capturing much of the annual and monthly anomalies. Biases are seen largely in the extremes, such as a failure of the reconstruction to capture the hottest and coldest monthly anomalies in the NH midlatitudes (summer warming and winter cooling over the NH continents) and an underestimation of the coolest monthly anomalies in the tropics (cooling near India and northern Africa). Mismatches are more widespread in the SH, however, where the reconstruction tends to be too warm on both a monthly and annual-mean basis. This can largely be attributed to mismatches over the Southern Ocean, discussed earlier. Precipitation arguably does better (Fig. 7a), but the reconstruction appears to underestimate the wettest and driest anomalies.

5. The LGM reconstruction

The LGM simulation is forced by reduced greenhouse gases, expanded ice sheets, and slightly reduced obliquity, with the longitude of perihelion similar to present day (Table 1). Because the change in orbit is comparatively small, the primary goal of this analysis is to separate the relative contributions of the greenhouse gases and ice sheets in LGM climate change.

In the LGM snapshot simulation, global mean 2-m air temperature cools by 5.3°C compared to preindustrial, with the largest changes over the new or expanded ice sheets (Fig. 8a). In general, continents cool more than oceans at the same latitude and, other than over areas of sea ice and NH high-latitude continents, temperature anomalies do not vary much by season. Precipitation change is characterized by a southward shift of the ITCZ, eastward shift of the South Pacific convergence zone (SPCZ), and a general drying over Indonesia and the western equatorial Pacific (Fig. 9a).

Fig. 8.
Fig. 8.

Change in annual-mean 2-m air temperature (°C) for LGM-preind in the (a) snapshot experiment and (b) reconstruction. The reconstruction may be separated into its components, two of which are shown: annual-mean 2-m air temperature anomalies due to changes in (c) greenhouse gases and (d) ice sheets. Obliquity and precession also affect temperature, but those changes are small in comparison. (e) The reconstruction-snapshot mismatch, showing the anomaly for (b)–(a).

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

Fig. 9.
Fig. 9.

As in Fig. 8, but for annual-mean precipitation (mm day−1).

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

The reconstruction does a relatively good job replicating the patterns of LGM temperature change (Fig. 8b). Extensive cooling occurs over the expanded ice sheets and the continents are generally cooler than the oceans. However, the reconstruction is too cold in general, with a global mean temperature decrease that is 0.9°C larger than the snapshot anomaly. This mismatch is worst over areas of sea ice, particularly the Barents Sea, Bering Sea, and the Southern Ocean south of the Atlantic and Pacific. These areas are prone to a shortcoming of the linear reconstruction methodology. In response to reduced CO2, sea ice grows in these high-latitude oceans, cooling the climate through increased albedo. However, in the ice sheets experiment, ice sheets are imposed in some of these same areas, which also reduces albedo. Adding these two effects together, as is done in the linear reconstruction, is nonphysical, as only one of these two responses can occur at any given point: ice sheets or growth of sea ice, but not both. While this limits the accuracy of the linear reconstruction, it hints at the potential importance of ice sheet extent on climate sensitivity, since ice sheets can limit where sea ice is allowed to grow. Brady et al. (2013) find a similar result: ice sheets damp the climate response to CO2 by limiting the area in which sea ice can grow. Brady et al. (2013) also suggest that downslope winds from the ice sheets warm the northern oceans and inhibit sea ice growth. As a side note, if ice sheets are unchanged, studies find that the climate may be more sensitive to doubled CO2 when starting from a lower CO2 concentration (Kutzbach et al. 2013; Brady et al. 2013).

Of course, when CO2 is reduced with a glaciated background climate, sea ice could simply grow farther south, counteracting the previously described effect to some extent, so additional research is needed. Additional CO2 sensitivity simulations, conducted over a range of ice sheet conditions, would be useful for investigating this. One such experiment set was conducted with the IPSL-CM4, in which the same CO2 increase was imposed with two different background states: preindustrial and LGM (Laîné et al. 2009). With preindustrial background conditions, increasing greenhouse gases from LGM to preindustrial levels increases global mean temperature by 2.4°C; when background conditions are like the LGM, the same change in greenhouse gases increases global mean temperature by only 2.0°C. Laîné et al. (2009) finds that decreased climate sensitivity with LGM conditions results from a weaker ice–albedo feedback due to differences in land and ocean cover, as suggested above, as well as changes in cloud feedbacks and ocean advection. In both Laîné et al. (2009) and the present research, large differences in temperature change occur over areas of NH sea ice, but the global mean temperature anomaly in Laîné et al. (2009) (−0.4°C) is only about half that of the reconstruction’s mismatch (−0.9°C), suggesting that other factors may account for some of the present mismatch. Because climate sensitivity is sometimes estimated based on glacial–interglacial temperature variations (e.g., Lea 2004), understanding the dependence of climate sensitivity on the background climate state may be beneficial to predictions of future climate change as well.

Proxy data also suggest that the LGM climate may have had reduced climate sensitivity. A comparison of climate sensitivity estimates from various proxy data over the past ~65 million years shows relatively consistent values, but estimates of LGM sensitivity tend to be a little lower than present sensitivity (PALAEOSENS Project Members 2012). The smaller cooling of the LGM snapshot simulation compared to the reconstruction potentially supports the idea that climate sensitivity is reduced when ice sheets are large. That said, it is difficult to estimate how much of the reconstruction’s cold bias may be due to this effect. Significant temperature mismatches also occur near areas of sea ice in the mid-Holocene experiment, which has no changes in ice sheets, so sea ice may simply be difficult to approximate with a linear reconstruction method.

Regardless of the true extent of the nonlinear effects, these experiments allow for a comparison of the relative impacts of greenhouse gas and ice sheet forcing. Greenhouse gases provide a more zonally consistent response, with temperature anomalies ranging from less than −2°C in low-latitude oceans to more than −6°C in the Arctic (Fig. 8c). Compared to this, the temperature response to ice sheets is much larger over the expanded ice sheets but generally smaller everywhere else, especially over the North Pacific and Labrador Sea (Fig. 8d). The global mean contribution of each forcing is similar: −2.9°C for the greenhouse gas component and −3.2°C for the ice sheets component, suggesting that greenhouse gases and ice sheets contributed nearly equally to the global mean cooling at the LGM. In the tropics, the temperature contribution from ice sheets is −1.7°C, compared to −2.2°C from greenhouse gases. This opposes the traditional view that ice sheets had little effect on tropical temperature change (e.g., Lea 2004; Schmidt et al. 2014) and suggests that ice sheets must be considered when estimating climate sensitivity from glacial-cycle tropical temperatures. In comparison, direct contributions from obliquity and precession to the global mean temperature change are small: −0.11° and 0.01°C, respectively.

The reconstruction also does an adequate job capturing the main features of the precipitation response, though it tends to overestimate the Pacific anomalies (Fig. 9). The reduction of greenhouse gases results in a general drying of the tropics, with the largest changes occurring along the equator and in the western Pacific. This precipitation response is similar (though opposite in sign) to precipitation changes in increased CO2 experiments (Bony et al. 2013; He et al. 2014) suggesting similar mechanisms at work. Bony et al. (2013) finds a general “wet-get-wetter, dry-get-drier” pattern in an increased CO2 experiment, partly caused by the temperature-driven increase of specific humidity.

In response to expanded ice sheets, the Pacific ITCZ shifts south, the SPCZ shifts east, and precipitation over Indonesia is reduced. The southward shift of the ITCZ is consistent with other experiments with a relatively cooler NH (e.g., Broccoli et al. 2006) and suggests that ice sheets may explain practically all of CM2.1’s southward shift of the ITCZ at the LGM. Glacial forcings also have a pronounced effect on monsoons (Table 3). In the LGM snapshot experiment, the Asian, North American, and South American monsoons weaken while the other regions show little change. Ice sheets generally produce the largest contribution to these decreases, with additional weakening in some regions due to the reduced greenhouse gas concentrations. Decreased water vapor due to the colder temperatures, as well as thermodynamic effects, may be responsible for these changes in LGM monsoons (Braconnot et al. 2007b). Changes in orbit at the LGM are relatively small, so obliquity and precession do not contribute much to precipitation changes. Early work supports the idea that, to a large extent, the response of some monsoons can be regarded as a linear combination of responses to individual forcings (Prell and Kutzbach 1987).

Table 3.

As in Table 2, but for LGM-preind. Change in summer precipitation (JJA in NH, DJF in SH) for LGM-preind snapshot, reconstruction, and components due to obliquity, precession, greenhouse gases (GHGs; CO2 and CH4), and ice sheets (mm day−1). While precession can have a large effect on monsoons, its effect at LGM is small because longitude of perihelion is similar at LGM (114.42°) and the preindustrial period (102.93°), since it has gone through almost one whole precession cycle. The regions are as in Table 2.

Table 3.

Scatterplots comparing the reconstruction to the snapshot experiment show general correlations but also some biases (Figs. 6 and 7). The temperature reconstruction is typically too cold, especially in the coldest extremes, with large mismatches occurring near regions of sea ice such as the Barents, Bering, and Labrador Seas and the western Southern Ocean during local summer and the surrounding months. The precipitation reconstruction tends to overestimate changes in the positive and negative extremes, such as the drying in the western equatorial Pacific.

6. LGM and mid-Holocene discussion

To put the results of CM2.1 in context with the broader modeling community, comparison can be made to CMIP5 simulations. Ensemble-mean temperature (Fig. 10) and precipitation (Fig. 11) anomalies are given for the mid-Holocene (eight models) and the LGM (five models).

Fig. 10.
Fig. 10.

Change in annual-mean near-surface air temperature anomalies (°C) in CMIP5 ensembles for (a) 6ka-preind (eight models) and (b) LGM-preind (five models). Anomalies that are not significant among the CMIP5 models at the 0.05 level, according to a paired two-tailed t test, are hatched.

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

Fig. 11.
Fig. 11.

As in Fig. 10, but for annual-mean precipitation (mm day−1).

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

For temperature, CM2.1 is relatively consistent with the CMIP5 ensemble for both annual-mean and monthly values (not shown). However, a notable difference at 6 ka occurs over parts of the Southern Ocean and Antarctica, where CM2.1 shows areas of cooling but the CMIP5 ensemble shows warming. At the LGM, the CMIP5 ensemble does not achieve the same cold extremes as CM2.1 over the new NH ice sheets, but the results are otherwise relatively consistent.

For mid-Holocene precipitation, anomalies in the CMIP5 ensemble are relatively similar to CM2.1 results over land (Fig. 11a). Monsoons generally show a strengthening in the NH and weakening in the SH. Over the ocean, CM2.1 and CMIP5 show similar shifts in Atlantic and Indian Ocean precipitation, but the patterns of change differ in the Pacific: among other differences, the CMIP5 ensemble shows more of a southward shift of the SPCZ at 6 ka, although parts of this signal are not significant among the CMIP5 models.

For LGM precipitation, the CMIP5 ensemble and CM2.1 again show similar changes over land. Over the ocean, the CMIP5 ITCZ shows a southward shift but, compared to CM2.1, the wet anomaly extends farther west and the SPCZ is not as dry. In general, however, CM2.1 is relatively consistent with the results of other models, suggesting that the climate responses discussed in the previous sections might not be overly model dependent.

While the model reconstructions do an adequate job approximating the climate response in many respects, they are deficient in some other areas. Other than features already discussed, the reconstructions are poor at approximating changes in the AMOC. For mid-Holocene, the snapshot experiment shows a small increase in maximum AMOC strength, while the reconstruction shows a change near zero (Figs. 12a,b), with changes due to obliquity and precession largely cancelling out. Changes in maximum overturning are listed in the Fig. 12 caption. At the LGM, the snapshot simulation shows an AMOC strengthening of 7 Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1) while the reconstruction shows a strengthening of 10 Sv (Figs. 12c,d), with the ice sheet component causing a much larger change than the other components. The reason for these mismatches is unclear, and more work must be done to properly simulate AMOC changes in models; the sign of LGM AMOC anomalies is not consistent among models from either PMIP (Weber et al. 2007) or PMIP2 (Otto-Bliesner et al. 2007). Inconsistencies in the AMOC response may be related to the failure of the reconstruction to capture sea ice changes, due to the importance of the salinity flux on AMOC strength. Alternately, AMOC strength may continue to adjust if the simulations were run longer.

Fig. 12.
Fig. 12.

Change in annual-mean AMOC (Sv) for the (a) 6ka-preind snapshot, (b) 6ka-preind reconstruction, (c) LGM-preind snapshot, and (d) LGM-preind reconstruction. Note the differences in scale. For 6ka-preind, changes in maximum overturning are 1.13 Sv for the snapshot and −0.06 Sv for the reconstruction (with −0.33 Sv for the obliquity component and 0.27 Sv for the precession component). For LGM-preind, changes in maximum overturning are 7.01 Sv for the snapshot and 10.01 Sv for the reconstruction (with −1.93 Sv for greenhouse gases, 11.11 Sv for ice sheets, 0.25 Sv for obliquity, and 0.00 Sv for precession). Stated changes in maximum overturning do not correspond directly to changes shown in the figure because locations of maximum overturning do not need to be coincident. Changes in maximum overturning in each component do not necessarily sum to the change in the reconstruction for the same reason.

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

Simulations of additional time periods would offer a more comprehensive test of the methodology presented here. For example, the linearity of the climate response to ice sheets could be tested by simulating a time period when ice sheets were at a size between that of the LGM and preindustrial, or smaller than preindustrial such as the Eemian. Yin et al. (2009) find that the patterns of climate response to NH ice sheets may not change significantly as the ice sheets grow, but generally increase in magnitude with larger ice sheets. Still, significant nonlinearities may occur at certain times, such as during the exposure or submersion of the Sunda Shelf (e.g., Bush and Fairbanks 2003), so further analysis is required.

7. Proxy time series reconstructions

To determine how well the single-forcing climate responses are supported by data, time series linear reconstructions are computed and compared against proxy temperature records. These time series reconstructions are made similarly to the snapshot reconstructions, but the calculations are preformed every 1 ka, using records of time-varying forcings rather than single values. The calculations are made globally, but results are here analyzed at the locations of specific proxy records. The records chosen for this comparison are two ocean sediment cores and two ice cores: TR163-19 from the eastern equatorial Pacific (Lea 2004), ODP806b from the western equatorial Pacific (Lea et al. 2000), the Vostok ice core (Petit et al. 1999), and the Greenland Ice Sheet Project 2 (GISP2) core (Alley 2000). The calculated linear temperature reconstructions will not account for any climate variations not directly driven by the long-term climate forcings and cannot capture faster-scale variability. That said, the linear reconstructions match the long-term temperature variations in the proxy records with moderate success (Fig. 13).

Fig. 13.
Fig. 13.

Change in temperature (°C) determined from proxy records compared to time series reconstructions at those locations. (a) SST from Mg/Ca in ocean sediment core TR163-19 [eastern equatorial Pacific; Lea (2004)], (b) SST from Mg/Ca in ocean sediment core ODP806b [western equatorial Pacific; Lea et al. (2000)], (c) air temperature from deuterium in Vostok ice core (Petit et al. 1999), and (d) surface temperature from GISP2 ice core (Alley 2000). The proxy record (thick black) is compared to a linear time series reconstruction (dotted blue). The linear reconstruction is the sum of components from obliquity (red), precession (orange), greenhouse gases (green), and ice sheets (gray), showing temperature difference relative to an idealized zero eccentricity state. While the reconstruction was calculated with a 1-ka time resolution, it is here regridded to the time axes of the proxy records. The mean temperature difference between the proxy record and the reconstruction has been removed from each proxy record, resulting in the proxies not having values of 0 at the present.

Citation: Journal of Climate 28, 24; 10.1175/JCLI-D-15-0329.1

The total range of temperature variations is well captured for the western Pacific core (Fig. 13b), but it is underestimated for the eastern Pacific core (Fig. 13a). In particular, the full warmth of the previous interglacials is not captured, partially because the greenhouse gas and sea level values of the chosen records do not rise far, if at all, above preindustrial levels. Some of the faster variability is also poorly accounted for, such as the SST changes during marine isotope stage (MIS) 5a-e in the eastern equatorial Pacific core. However, the otherwise decent fit suggests that the single-forcing simulations are relatively consistent with recorded paleoclimate changes. Looking at the components of the reconstructions suggests the extent to which each forcing contributed to the total change. In the two Pacific cores, changes in greenhouse gases provide the largest contribution, but ice sheets also appear to have a considerable impact (see also Fig. 1). The direct effects of orbital changes are minor in comparison, with the effect of obliquity almost nonexistent.

The Vostok reconstruction shows significant departures from the proxy record, but also reveals a way in which this kind of comparison can be useful. The largest mismatches between the proxy record and the model-based reconstruction appear to be in phase with obliquity variations (Fig. 13c). When obliquity is low (providing a cooling effect to Antarctica), the reconstruction is generally too cold compared to the proxy record, and when obliquity is high (providing a warming effect), it is generally too warm. Two possible explanations for this mismatch are that the model produces too large of a direct response to obliquity or that the response to obliquity is damped when ice sheets are large or CO2 is low. Regarding the first possibility, obliquity has a significant effect on local annual-mean insolation so, while the model may still produce too large of a response, a sizable direct temperature response is expected. The second possibility requires further investigation, but could be looked into using something like the emulator described in Araya-Melo et al. (2015).

The reconstruction for the GISP2 ice core illustrates several shortcomings of the current methodology (Fig. 13d). As formulated, reconstructions will only include climate variations that are linearly related to variations in orbital geometry, greenhouse gas concentrations, and ice sheet volume. Thus, the linear reconstruction methodology will not reproduce the millennial-scale variability that is evident in the GISP2 record, which has been associated with changes in ocean circulation, perhaps in response to ice sheet freshwater discharge (Jackson et al. 2010; Dokken et al. 2013). However, differences between the linear reconstruction and proxies may prove useful for identifying the portions of records that require additional explanation.

Finally, it should be noted that changes in CO2 and ice sheets are not truly forcings in the current orbital theory of climate change. Instead, they are more accurately regarded as slow feedbacks that respond to insolation anomalies caused by Earth’s orbital variations. When viewed in this context, the Earth system has obvious nonlinearities, and the current paper’s discussion of linearity should be considered with that in mind. However, current generation climate models generally lack interactive ice sheet and carbon cycle components, so changes in CO2 and ice sheets are often regarded as forcings. As climate models continue to develop, the interactions between orbital forcings and slow feedbacks in the climate system will certainly be explored in greater depth.

8. Conclusions

In this paper, idealized equilibrium simulations are analyzed to determine the individual effects of orbital, CO2, and ice sheet forcings on the climate system. To investigate the degree to which past climate change can be considered a linear combination of responses to individual forcings, these idealized simulations are scaled and combined to create linear reconstructions of past climate change, which are compared against 6-ka and LGM snapshot experiments as well as temperature records from ocean sediment cores and ice cores. In places where a linear reconstruction does an adequate job approximating past climate change, the components of the reconstruction give an estimate of the relative contributions of different forcings in the past climate response. From this research, the following conclusions can be made:

  • Linear climate reconstructions do a reasonable job approximating many aspects of past climate and suggest that much (but not all) of CM2.1’s total climate response may be accounted for by a sum of responses to individual forcings. This is consistent with the relative linearity suggested by several past studies (Felzer et al. 1998; Jackson and Broccoli 2003) and reinforces the usefulness of idealized single-forcing experiments in understanding aspects of climate change.
  • Changes in greenhouse gases and ice sheets contribute nearly equally to global mean cooling in the LGM reconstruction, each lowering the mean temperature by ~3°C, although the reconstruction overestimates cooling by almost a degree. Unlike other studies, ice sheets contribute notably to the cooling in the tropics and SH, suggesting that tropical paleoclimate variations should not be considered a response to greenhouse gases alone.
  • Climate sensitivity may be influenced by the size of ice sheets. A CO2 reduction may cool the climate further when imposed on a climate system with preindustrial ice sheets compared to one with LGM ice sheets. This dependency could result from changes in the strength of the ice albedo feedback as well as changes in cloud feedbacks and ocean advection (Laîné et al. 2009). Because of this, care is required when trying to determine CO2 climate sensitivity from past climate changes.
  • Monsoons in CM2.1 are generally well captured by the linear reconstructions. At 6 ka, strengthened NH monsoons and weakened SH monsoons are primarily a response to precession. At LGM, ice sheets weaken the Asian, North American, and South American monsoons, while lowered CO2 weakens the Asian, South American, and southern African monsoons. The southward shift of the ITCZ at LGM is primarily a response to expanded ice sheets, while reduced greenhouse gases cause some reduction in equatorial precipitation.
  • Regions of the largest temperature differences between reconstructions and snapshot experiments are generally near areas of sea ice, emphasizing potential sea ice response nonlinearities. AMOC changes are also poorly captured by the linear reconstructions.
  • Linear reconstructions capture the long-term temperature changes in proxy records relatively well, but also highlight climate responses that require additional study to understand, such as the apparently reduced obliquity variations in the Vostok record.
While considerable differences do exist in the linear reconstructions compared to the snapshots and proxy records, the overall similarities are encouraging, supporting the use of idealized single-forcing simulations for understanding aspects of past and potential future climate change. However, areas of disagreement should be considered further, as they may indicate important nonlinearities in the regional or even global climate response, or limitations in our understanding of climate processes.

Acknowledgments

The authors thank F. Zeng and J. Krasting for guidance in running the GFDL CM2.1; B. Raney, F. Zeng, and M. Khodri for additional simulations; D. Pollard for aid in calculating the calendar conversions; and D. Lea for help in choosing high-quality time series records. Additionally, we thank the NOAA/Geophysical Fluid Dynamics Laboratory at Princeton for computational and modeling resources and three anonymous reviewers whose comments helped improve this paper. This research was supported by a postdoctoral fellowship from the University of Texas Institute for Geophysics, as well as a grant from the National Science Foundation as part of their Paleo Perspectives on Climate Change program (Grant ATM0902735).

APPENDIX

Linear Reconstruction Equations

The equations used to compute linear reconstructions are below. The variable X represents the model output of any climate field, while ΔX quantifies the change in that quantity due to a forcing or set of forcings. Explanation of the terms and calculations follow:
eq2
eq3
eq4
eq5
eq6
eq7
eq8
eq9
eq10
eq11
In the above equations, the orbital parameters (, , and ), CO2, CH4, and Δsealevel are the forcings of the desired climate; is the value of obliquity; is longitude of perihelion (where = 0 indicates perihelion at the NH autumnal equinox and larger values, from 0° to 360°, indicate perihelion later in the year); and is eccentricity. The subscripts low, high, AE, WS, VE, SS, 0ecc, HalfCO2, IceSheets, and preind indicate output or forcing parameters from those simulations, and is the increased value of eccentricity (0.0493) used in the precession simulations. The terms CO20, CH40, and N2O0 represent the preindustrial simulation’s greenhouse gas values of 285.978 65 ppm, 804.9 ppb, and 275 ppb, respectively. Past relative sea level is used as an analog for past change in ice sheet volume, so the ice sheet response is scaled by the desired relative sea level (cf. preindustrial) divided by the relative sea level in the LGM simulation, which is approximately −125 m for ICE-5G (Peltier 2004).

In making the reconstructions, the 0ecc simulation is considered the base, and the climate anomalies due to each change in forcing (, , and ) are calculated. The obliquity and precession response patterns are scaled by their respective orbital parameters. For precession, the term is necessary to account for the climate response to altered eccentricity, regardless of precession (increased eccentricity raises global, annual-mean insolation regardless of the longitude of perihelion). For greenhouse gases, a halving of CO2 results in a radiative forcing of approximately −3.71 W m−2 (Myhre et al. 1998), so the HalfCO2-preind output is divided by −3.71 to normalize for radiative forcing, then multiplied by the radiative forcing of the desired changes in CO2 and CH4, as calculated with equations from Table 6.2 of the IPCC TAR (see Ramaswamy et al. 2001). For ice sheets, relative sea level may not be the ideal scaling factor, but it is used here because time series of this variable can be determined from proxy records. For the snapshot reconstructions, the Δsealevel variable is specified to add either none (for preindustrial or 6 ka) or all (for LGM) of the effect of LGM ice sheets to a reconstruction.

Using the above equations, a linear climate reconstruction, as well as the contribution from each forcing term, can be calculated for any combination of orbital, CO2, CH4, and (with limitations) ice sheet forcings. When calculating a single snapshot, specific values are used for the variables. When computing a time series, a reconstruction is computed every 1 ka using time-varying forcing records.

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