1. Introduction

The basic forcing for the climate system is the radiation received at the top of the atmosphere. The large-scale and low-frequency variations of insolation are determined by the orbital parameters obliquity, eccentricity, and the longitude of perihelion (precession), and there is ample evidence (Imbrie 1984; Herbert and Fischer 1986; Olsen 1986; Pisias et al. 1995) that the earth’s climate experiences changes at these “Milankovitch” frequencies.

The question of how orbital change is translated to the paleoclimatic record has been studied for several decades (Hays et al. 1976; Saltzman and Sutera 1984; Hyde and Peltier 1987; Short et al. 1991). Explanations exist for some of the power seen in the paleoclimate record but there are still numerous areas of uncertainty. For example, the strong 100 kyr signal observed in the climate record over the past 900 kyr has been attributed to the interaction of ice sheets and seasonality (Hyde and Peltier 1987; Tarasoff and Peltier 1997). Precession plays a critical role in these interpretations. Since precession redistributes insolation through the year without affecting the annual average, a rectification mechanism is clearly required to produce nonzero annual average forcing from this purely seasonal input. The studies mentioned above demonstrate that ice-sheet variations can provide such a mechanism. However, deep sea cores show evidence of precessional power even at times when there was little or no land ice (Pisias et al. 1995), so it appears that there are other rectification mechanisms in the climate system. One purpose of the present work is to investigate the possibility that the thermohaline circulation of the global ocean may act as a rectification mechanism to generate low-frequency signals from variations in the amplitude of seasonal forcing.

Zonally averaged “2½”-dimensional thermohaline models coupled to simple energy balance models (EBMs) of the atmosphere have had considerable success both in reproducing the current state of the ocean and in providing plausible mechanisms for various paleoclimatic events such as the Younger Dryas (Wright and Stocker 1991) and Dansgaard–Oeschger oscillations (Sakai and Peltier 1995). A weakness of such models, however, lies in their zonally averaged representation of the atmosphere, which does not resolve the land–sea contrast in surface temperature (Hyde et al. 1989). This contrast is potentially important for at least two reasons. First, a larger signal in air temperature is expected over land than over the oceans so a zonally averaged EBM will underestimate the observed terrestrial signal. Second, it seems plausible that zonal variations in surface air temperature may affect the stability of the thermohaline circulation. For example, a decrease in the strength of the overturning circulation in the Atlantic basin will be accompanied by a decrease in the surface temperature at high northern latitudes, and this will tend to reinforce (hence stabilize) the overturning within this basin. Since zonal averaging will reduce the magnitude of the atmospheric temperature variations by artificially spreading them around the globe, it is possible that such averaging affects the stability of the thermohaline circulation.

In this paper we describe a coupled atmosphere–ocean climate model containing longitudinal resolution in both the ocean and atmosphere, and examine the results from a 3.2 Myr model “paleo-integration.” The coupled model divides the earth into six north–south atmospheric stripes, and three ocean basins coupled through a circumpolar southern ocean. The evolution of both temperature and salinity, averaged over the width of each basin, is modeled, but only temperature results are discussed here. Effectively, the model describes the climate on a “beachball” earth, where each stripe contains an atmosphere overlying ocean or land depending on latitudinal position. The Wright–Stocker ocean model was used to compute the ocean’s thermohaline circulation, and a six-basin energy balance model is developed to represent the atmosphere. The resulting idealized climate system is illustrated in Figs. 1 and 2.

At the top boundary of the model the atmosphere receives net solar radiation Q_N and emits longwave radiation OLR as a function of its temperature [i.e., OLR = f(T)]. Here Q_N is a function of the planetary albedo and the incoming solar radiation. In this paper we take the albedo to be fixed at the current annually averaged climatology. Therefore, Q_N depends solely on the orbital parameters of the earth so that we will consider only the effects of changes in incoming radiation on the coupled system. As well, we run the model in ice-free mode in order to isolate the effects of ocean circulation and convection on the climate system. Clearly, this model is only one of a possible heirarchy of coupled models, but the results presented here should represent a useful benchmark for comparison with the results from future studies.

The outline of this paper is as follows. Section 2 describes the atmosphere–ocean model in more detail. The next section discusses the setup of the paleo-integration and issues relevant to it. Section 4 reports model results and highlights questions arising from the paleo-integration. These questions are answered in sections 5 and 6 with the aid of an even simpler atmosphere–ocean box model. A summary and conclusions are presented in the last section.

2. The atmosphere–ocean climate model

In this section we discuss the coupled model geometry, the atmosphere and ocean model components, the coupling procedure, and the comparison between the model estimate of the current climate and the actual current climate.

b. The atmospheric model

The ocean model is essentially unchanged from that discussed in previous publications (Wright and Stocker 1991; Stocker et al. 1992b) and details will not be repeated here. The inclusion of zonal resolution in the atmospheric EBM is new and hence our discussion focuses on this feature and the ocean–atmosphere coupling.

The atmospheric model describes the evolution of the surface temperature (T_ij) as a function of latitude (j) for each of the zonally averaged basins (i). Interbasin exchange is a function only of the temperature difference between basins. The model allows for both diffusive and advective fluxes in the horizontal, but the version used here was purely diffusive. Air–sea exchange is determined precisely as in Stocker et al. (1992b). The governing equation for basin i at latitude j is

View Expanded

where Q_N is the net solar radiation, OLR is the outgoing longwave radiation, F_OA is the flux from ocean to atmosphere, κ is the diffusivity in the north–south (ns) or east–west (ew) direction, R is the earth’s radius, ρ is density, C_P is specific heat, H is the scale height of the atmosphere, ϕ is latitude, and λ is longitude. In the model run considered here, we take

Q_NαϕQϕ, t(2)

where Q(ϕ, t) is the shortwave radiation at the top of the atmosphere and α is the planetary albedo. The outgoing longwave radiation is given by

AϕBT_ij(3)

where B is a constant set equal to 2 W m⁻² °C⁻¹. We calculate α(ϕ) using satellite data for Q_N, and A(ϕ) is estimated using data for OLR and the zonally and annually averaged temperature. (Here A and α were taken to be functions of latitude only due to data availability at the time the model was first run.) Note that the atmospheric model just described has tunable parameters:the horizontal diffusion terms (viz., κ_ns and κ_ew), and coefficients in the air–sea coupling term F_OA. These are determined as discussed below.

c. Atmosphere–ocean coupling

Our goal is to couple the atmosphere to the ocean in a way that produces a stable climate that resembles the current climate in its major characteristics (e.g., zonally averaged ocean circulation and atmospheric temperature fields). To do so, we use the technique developed by Stocker et al. (1992), adapted to account for the multibasin atmospheric model. In this method, the ocean is first spun up to equilibrium with the surface temperature and salinity fields restored to the present-day annually and basin-averaged values of Levitus (1993) on a timescale of 50 days. At the end of this spinup period, the ocean surface fluxes of heat and moisture (represented in our rigid-lid model as a virtual salt flux) are diagnosed and used as the bottom boundary conditions for the atmospheric model.

The coupling proceeds in three stages. First, a zonal and annual average of (1) is performed, which yields

View Expanded

where quantities with a subscript j represent zonal averages around the entire globe. Note that the simple form of this equation depends on the linearization of the OLR term.

The values of F^j_OA are determined by the surface fluxes across the ocean surface at the end of the initial ocean-only spinup period and Q_N, T_j, A, and B are estimated from observations. Thus, (4) can be trivially solved for κ_ns(ϕ). Next, we want to determine values of κ_ew to be consistent with the climatological, annually averaged temperatures T_ij. This was done using an optimization routine that forward integrates (1) to equilibrium finding the κ_ew that minimizes the “squared error” between the T_ij data and the final equilibrium temperatures. The“squared error” includes a contribution that penalizes nonphysical diffusivities. Note that κ_ew (as well as κ_ns) could, in principle, be a function of ϕ, λ, T, etc., but for this study we have chosen to consider only κ_ew = const and κ_ew = κ_ew(ϕ).

Finally, with the atmosphere and ocean coupled and adjusted to a steady state, the ocean surface flux, previously derived from an ocean-only spin up, can be converted to a true interactive coupled ocean–atmosphere flux of the form F_OA = net solar flux + net infrared flux + sensible heat flux + latent heat flux. That is [following Stocker et al. 1992, their Eq. (17)], for the ijth basin,

View Expanded

where a is the atmospheric absorptivity, ϵ represents emissivity, D the sensible heat flux exchange coefficient, E = c_ef(T_m, T_a) the evaporation [f is specified as in Stocker et al. (1992)], and the subscripts m and a stand for mixed layer and atmosphere, respectively. In principle, a, ϵ_o, ϵ_m, ϵ_a, D, and c_e could each be treated as free parameters to be determined by the optimization procedure. However, we have followed the more pragmatic method introduced by Stocker et al. (1992) in which a, ϵ_o, ϵ_m, D, and E are determined from climatological data, then c_e is determined to be consistent with the bulk formula for evaporation and ϵ_a is determined by (5).

The above procedure produces an atmosphere and ocean that are coupled and in steady state with respect to annually averaged quantities. This result is satisfactory for many coupled atmosphere–ocean problems. However, for our present purpose it is necessary that the seasonal cycle be included in the solar forcing. Unfortunately, an atmosphere and ocean that are in equilibrium with annually averaged forcing do not necessarily remain unchanged, even in their annually averaged properties, when a seasonal cycle is introduced. The problem of optimized coupling with seasonal variations included is currently being investigated. In the meantime, the parameter determination and coupling procedure discussed above was considered to be a reasonable starting point for integrations that include seasonally varying radiative forcing. After the model was coupled, the seasonal cycle in shortwave radiation was initiated and the model was run in fully interactive mode for a 5 kyr equilibration period. The model was thus adjusted to the current seasonally varying forcing before beginning the paleo experiment (i.e., before changing the orbital parameters to those corresponding to a different epoch).

3. The paleoclimate experiment

The model run used to investigate the response to long-term changes in orbital forcing was conducted as follows. First, the ocean and atmosphere components of the model were coupled and run to equilibrium under current climatology, including the current seasonal cycle in incoming shortwave radiation. After an equilibrium state under present-day conditions was achieved, the orbital parameters controlling solar radiation at the top of the atmosphere—eccentricity, obliquity, and “precession”—were set to values corresponding to some time in the past and the integration was continued with the orbital forcing continually updated.

It was found that model results at time t were not sensitive to the start time, t₀, for the paleo-integrations provided t − t₀ was greater than a few thousand years. That is, the model lost memory of its initial conditions over a timescale of a few thousand years. This result clearly depends on the fact that the system did not undergo any major mode transitions. This is a useful result since it means that shorter runs (on either the same or different machines) can be “stitched” together into one long run. In practice, model runs were overlapped by 5 kyr and the initial 5 kyr of each run were discarded (after verifying agreement with the previous run at the end of this period). In this manner, a continuous time series extending over 3.2 Myr was generated. The model was integrated asynchronously, with an ocean time step of 20 days, and an atmospheric time step of 2 days. (An implicit numerical scheme was used in the atmospheric integration in order to allow the 2-day time step.) Data was stored typically every 200 yr, with occasional periods of 2- or 20-yr output.

4. Results from the paleoexperiment

Figure 7 shows a sample of relevant variables from the model run. Plotted are annual and global averages of the net solar radiation, air temperature, and ocean temperature. The last two panels show the annual average maximum overturning streamfunction in the Atlantic basin (Atl_circ) and insolation at northern winter (band 45°–75° lat). The latter is a measure of the precessional contribution to the radiative forcing. Amplitude spectra for these quantities are plotted in Fig. 8.

The following points are of interest:

1. The global air temperature is almost a perfect mirror of Q_N, except that it has small amplitude higher-frequency variability superimposed on it. Closer inspection of the data show that this variability has a period of about 100 yr and is related to slight changes in ocean circulation and convection. The amplitude spectra show energy in the 40 kyr (obliquity), and the 100 kyr and 400 kyr (eccentricity) bands.

2. The global ocean temperature has significant energy in the 20 kyr (precessional) band, as well as the 40 kyr band. At 40 kyr we see from the raw data that the ocean and atmosphere temperatures are anticorrelated. We will show that this is due to the spatial distribution of the obliquity forcing plus oceanic convection.

   With respect to the power at 20 kyr, the globally averaged energy equation

   

   

   View Expanded

   

   where V is volume and the other symbols have their usual meaning, raises the question: How can T_ocean contain significant energy in the 20 kyr band while T_atm and Q_N do not? We will refer to these two somewhat counterintuitive results as “the 20 kyr/40 kyr dilemma.”

3. The Atl_circ and T_ocean spectra are each similar to the northern winter (N-Wint) insolation in the 20 kyr band. Phase spectra show that T_ocean is 90° out of phase with the northern winter insolation, indicating that T_ocean acts as an integrator of the northern winter insolation.

4. The spectrum of T_ocean shows that the global ocean response in the eccentricity band is suppressed relative to the forcing Q_N. Phase spectra of T_ocean and Atl_circ (see later) show that T_ocean is approximately 180° out of phase with Atl_circ at periods less than 100 ky (i.e., low ocean temperatures occur coincident with stronger ocean circulation), but in phase in the eccentricity band.

In the next two sections we present physical explanations for each of these results aided by a highly simplified coupled atmosphere–ocean climate box model, which helps to illustrate and confirm these explanations. The 20 kyr/40 kyr dilemma is discussed first, followed by an explanation for why the global ocean’s response differs from the atmosphere’s at long periods.

5. The 20 kyr/40 kyr dilemma

a. The 20 kyr energy and ocean convection

The first question that we address is why the ocean response includes significant energy in the 20 kyr precession band, but the atmosphere does not. We hypothesize that this is due to the rectifying effect of convection in the ocean and then present results from a two-(north–south) basin three-layer climate model to support this idea. For brevity we relegate the details of this model to an appendix.

The most important point to be made is that convection serves as a mechanism to rectify seasonal cycle forcing such that amplitude modulation of the seasonal cycle results in deep ocean temperature variations at the modulation frequency, with very little effect on surface conditions. Figure 10 shows a schematic of the process. A seasonally low radiation input cools the mixed layer causing convection, which cools the deep ocean, moving a quantity of heat to the mixed layer–atmosphere. Due to the low thermal mass/fast adjustment timescale of the mixed layer–atmosphere this flux causes a rapid increase in temperature that is efficiently radiated to outer space. On the other hand, the deep ocean is effectively isolated from such rapid surface processes and the cooling effect accumulates over the years. Based on this idea, we expect that the changes in the deep ocean temperature, T_d, should be related to the precessional forcing, which controls the seasonality in polar radiation.

The general model, shown in Fig. 9, consists of equatorial and polar boxes, each with an atmosphere overlying an ocean mixed layer, and a deep ocean region. The fluxes between boxes are modeled as a transfer coefficient (q in W m⁻² K⁻¹) times a temperature difference, resulting in an exchange time between boxes given by τ ≡ (ρC_PL)/q, where L is a relevant length scale (either horizontal or vertical). The only nonlinearity in the model is a convection scheme whereby the timescale of vertical exchange is greatly reduced when the density gradient is statically unstable. This nonlinearity serves as the mechanism for rectification of seasonal cycle forcing.

To illustrate the rectifying effect of convection, it suffices to consider an isolated vertical column. Thus, we consider the results of numerical experiments performed with a simplified version of Eqs. (A1)–(A3) (the “global model”) in which the horizontal exchange terms are omitted. For these experiments, the paleonet radiative forcing was modeled to be similar to the paleoforcing for the beachball (WS) model, that is, as an annual-mean term that changes on a 40 kyr timescale and an amplitude-modulated seasonal cycle term representing a precessional 20 kyr effect with zero annual mean:

View Expanded

where Q = 230 and Q_prec = 100.

With convection turned off it was found, as expected, that all temperatures followed the mean paleoforcing

QtQπtk

Figure 11 shows the result with the convective scheme on. We see that T_d shows 20 kyr precessional power but T_a ≈ Q(t) with no (apparent) 20 kyr power. While we now see how the global ocean temperature can have oscillations in the precessional band, we seem, in light of the global energy Eq. (6), to again encounter the 20 ky dilemma.

Figure 12 is a plot of Q_N and OLR, (Q_N − OLR), and the convective flux from the global model. The top panel shows that (A + BT_a) is not a perfect 40 kyr sinusoid, the difference showing up as the 20 kyr signal seen in Fig. 12b. This 20 kyr signal is a reflection of the annually averaged convective flux—the rectification process—shown in Fig. 12c. The rapid adjustment of the mixed layer–atmosphere limits the magnitude of this effect, which means that the term (Q_N − OLR), the source of the 20 kyr power in T_a, is doomed to be the small residual of two large numbers.

Figure 13 shows that the deep ocean temperature looks like an “integrator” of the annual average convective flux or (Q_N − OLR) curve. When (Q_N − OLR) is negative, the deep ocean is giving up heat to the atmosphere and T_d declines. The opposite occurs when (Q_N − OLR) is positive.

We summarize these effects as follows. Changes in the seasonality in radiative forcing caused by the precession of the equinoxes lead to changes in convective fluxes in polar regions. The mixed layer–atmosphere respond quickly to a convective flux from the deep ocean, by heating up and thus slowing down convection (which depends on T_m − T_d in this model), and ultimately sending flux anomalies to outer space. The efficient radiation to space limits the annual average heat accumulation (or rectification) in the mixed layer–atmosphere so that precessional effects in this region are small compared to obliquity effects. On the other hand, the deep ocean, with its increased sensitivity to surface conditions at the coldest time of the year, and its long-term memory, integrates the sequence of “precessionally forced” convective “anomalies” leading to significant temperature changes in the 20 kyr band.

These features of the simple three-layer model also exist in the WS model. Figure 14 shows a high-resolution time series of global ocean temperature, (Q_N − OLR), and their amplitude spectra. The (Q_N − OLR) data are a complicated noisy signal that represents the previously mentioned high-frequency variability in T_atm. The series contains a burstiness with clear 20 kyr periodicity, also seen in the amplitude spectrum. In the WS model then, there is 20 kyr energy in the T_atm data, but it is very weak, as we might now expect.

Figure 15 shows the annual average fraction of convective cells from the WS ocean model together with the corresponding northern winter insolation. These signals have 20 kyr periodicity 180° out of phase with each other (i.e., there is more convection when the polar insolation is low and vice versa). Previously it was noted that T_ocean and northern winter insolation were 90° out of phase with each other in the 20 kyr band. If we take the fraction of convecting cells as a measure of the global convective flux, then we see that T_ocean acts as an integrator of the annual average convective flux just as it did in the simple three-layer convective model.

b. The 40 kyr energy and meridional variations in shortwave radiation

The above discussion uses a one-dimensional (1D) model to show how 20 kyr temperature variations can be significant in the ocean but negligible in the atmosphere. However, the anticorrelation between T_ocean and T_atm at obliquity frequencies could not be imitated by the 1D model: latitudinal resolution is required to explain this result. Obliquity forcing changes the latitudinal distribution of insolation with the equatorial and polar regions rising and falling out of phase with each other. The albedo distribution of the WS climate model results in global increases in net radiation at the same time that polar radiation is lowered. It seems possible then that increased convection due to lower polar radiation could cause the ocean temperature to fall coincident with increasing net shortwave radiation into the climate system. We used the complete version of the box climate model discussed in the appendix to test this hypothesis.

To simulate the radiation field described above, the net radiative forcing was chosen as

View Expanded

where δQ_N = (Q₂₂ + Q₁₂) represents the differential obliquity forcing and the cos(4πt/1.0) term in the equatorial box represents the two yearly passages of the sun in this region. The constants in (8) and (9) were chosen to be consistent with the paleoradiation field analyzed from the WS model. Canonical values for Q₁₂ and Q₂₂ are 1.4 and 3.6, respectively.

Figure 16 shows annual averaged T_a, T_d, and Q_N from a typical model run. We see that T_a again follows Q_N, T_d has 20 kyr precessional power, and that indeed the above net radiative forcing can cause the globally averaged ocean temperature to be anticorrelated with T_a at 40 kyr periods. It was found that the response of the model depended in a complicated way on δQ_N, the convective transfer coefficient q_conv, and the horizontal transfer coefficients in the mixed layer and deep ocean. However, because a polar–equatorial gradient in Q_N was necessary in all cases to produce the T_a:T_d inversion effect, we conclude that the particular spatial distribution of obliquity forcing in concert with oceanic convection is responsible for the 40 kyr atmosphere–ocean temperature anticorrelation seen in the global climate model.

6. The ocean response in the eccentricity band

As observed in Fig. 8 the response of the global ocean in the eccentricity band is suppressed relative to T_atm and the forcing Q_N. The reason for this behavior relates to the nature of insolation at long periods and the equation of state of seawater.

Solar insolation averaged over the year Q increases with increasing eccentricity. To lowest order this can be expressed as

View Expanded

where e is the eccentricity and Q_o is the average insolation at zero eccentricity.

If dynamics could be neglected, these changes would have roughly the same effect on atmosphere and ocean. The slowest significant frequency in the eccentricity variation corresponds to a period of 100 kyr—far larger than oceanic diffusive timescales. However, there are at least two mechanisms in a dynamic ocean that act in the opposite direction from diffusion and tend to weaken the deep ocean response.

To lowest order a change in eccentricity affects the annually averaged insolation by the same percentage throughout the globe. However, due to the higher albedo at high latitudes, this translates to a much smaller signal in watts per square meter absorbed at high latitudes (where deep water is formed) than it does over the globe as a whole. Insofar as convection is the major driving force for global ocean temperature changes, the deep ocean will show a smaller response to eccentricity forcing than will the atmosphere.

There is also a second, dynamic process that reduces the deep ocean response. Consider an ocean in equilibrium. Diffusion tends to heat the deep ocean, while the overturning circulation cools it by producing cold bottom water. If there were no circulation changes an eccentricity decrease would tend to cool the deep ocean by reducing the downward diffusion of heat, while an increase would have the opposite effect.

However, changes in eccentricity also affect the equator to pole density gradient and do so in such a way as to counter the change in diffusive heat flux to the deep ocean. For example, an eccentricity decrease will cool both equatorial and subpolar surface waters, but for the reasons outlined above, the cooling will be larger at the equator. In addition, the equation of state tells us that for a given (small) temperature change, the density change of warmer water will be larger than that of colder water. Thus an eccentricity decrease will result in a smaller pole to equator density gradient in surface waters and a weakening of the thermohaline circulation. The resulting dimunition in the supply of cold bottom water will allow diffusion from above to warm the deep ocean, offsetting to some degree the cooling caused by the eccentricity decrease.

Based on the above, we expect that as insolation decreases, the overturning circulation will slow down and the decrease in global ocean temperature will be correspondingly reduced. Thus Q_N, T_ocean, and Atl_circ should be in phase at eccentricity periods and the signal seen in T_ocean should be smaller than that seen in the mixed layer or the atmosphere. We have already noted from Fig. 8 that the deep ocean temperature variation at eccentricity periods is smaller than surface temperature variations. Figure 17 is a plot of the coamplitude spectra and phase for T_ocean–Q_N and Atl_circ–Q_N, which shows that the expected phase relations are indeed realized.

7. Summary and conclusions

It has been known since the days of Croll and Milankovitch that insolation changes due to orbital perturbations have a distinct latitudinal and seasonal signal. The frequency and amplitude of the thermal response to these perturbations, however, is modified by the multiplicity of time constants and nonlinear processes of the climate system. For example, while hundred-thousand-year power is weak in the orbital insolation variations, it is dominant in the ice volume record of the late Pleistocene.

While the ice sheets act as an important filter on the orbital input, other components of the climate system may be of equal importance. This paper investigated the filtering of the astronomical forcing by the thermohaline circulation using a low-order coupled atmosphere–ocean climate model. We found that, indeed, this filtering was significant.

The atmosphere–mixed layer and the deep ocean respond quite differently to precessional and obliquity forcing. Changes in the longitude of perihelion (precessional changes) do not alter the annually averaged insolation received at the top of the atmosphere, tending instead to alter the strength of the seasonal cycle. Years with colder winters are compensated with warmer summers and vice versa. Thus precessional changes have an almost negligible effect on the annually averaged atmosphere–mixed layer temperature. Deep ocean temperatures, on the other hand, are sensitive not to annually averaged forcing, but to the temperature of deep-convecting water and the frequency of deep convection. Since precession affects both of these through winter temperature changes in the convecting region, there is a strong precessional signal in annually averaged deep ocean temperatures.

Obliquity forcing changes the latitudinal distribution of insolation at the top of the atmosphere, with equatorial and polar regions rising and falling out of phase with each other, without changing the global average. However, the latitudinal form of the planetary albedo leads to global net radiation changes that are out of phase with polar regions. This forcing, with a convecting ocean model, leads to an anticorrelation between the global ocean and atmospheric temperatures at obliquity frequencies.

One might expect the long period eccentricity changes to affect the atmosphere and deep ocean equivalently, but the mechanism that sustains deep ocean temperature dictates otherwise. Two effects are identified. First, deep water is formed at polar latitudes, where eccentricity effects (in terms of watts per square meter absorbed) are relatively small, so the forcing felt by the deep ocean is correspondingly reduced. Second, eccentricity changes affect the pole-to-equator surface density gradient in such a way that the resulting circulation changes act to reduce the warming or cooling by diffusion from the surface. The net result is that the response of the deep ocean at eccentricity periods is suppressed relative to the atmosphere or the surface layer of the ocean.

Our simple model estimates globally averaged ocean and atmosphere temperature fluctuations of less than 0.2°. Zonally averaged values (around the entire globe) were three times this value and local values (averaged across an individual basin) two or three times larger again. Thus even local variations will not be much larger than 1° according to the present model. However, it is important to note that the results of this study are intended to demonstrate qualitative effects and quantitative estimates should not be taken very seriously. Numerous effects that might amplify temperature signals have been deliberately omitted in order to reveal qualitative tendencies in the simplest context. In particular, models that include a simple ice–albedo feedback can produce local air temperature variations of several degrees, an effect that could enhance deep convection and increase the amplitude of the deep ocean signal (e.g., Stocker et al. 1992a). Feedbacks associated with the hydrological cycle may even cause mode flips, which can result in dramatic global temperature changes (e.g., Manabe and Stouffer 1994; Nakamura and Marotzke 1994; Rahmstorf 1995). The effects of ice sheets, clouds, and changing wind fields can complicate the picture still further (e.g., Broecker 1994; Berger and Loutre 1997; Rahmstorf and England 1997).

In spite of the above caveats, it remains clear that the orbital signature can vary substantially in the vertical. In particular, seasonal variations will be largest (by far) in the atmosphere and the ocean mixed layer, but long timescale variations in the annually averaged temperature may actually be larger in the deep ocean as a result of rectification of the annual signal by deep convection. Consequently, benthic and planktonic forams in the same core might respond to quite different temperature changes, and even to different orbital parameters.

Though our results are too preliminary to be used directly in the interpretation of paleoclimatic data, it is clear that the thermohaline circulation acts as a strong filter on the Milankovitch forcing. Thus researchers should beware of drawing conclusions as to the validity of the Milankovitch theory on the basis of marine paleoclimatic records. Until we have a more complete understanding of the effects of orbital variations on the climate system, it will remain possible that two apparently contradictory records may in fact be in agreement.