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 A two-dimensional, one-basin thermohaline oceanic circulation (THC) model coupled to an atmospheric energy balance model (EBM) with land ice albedo effect and a thermodynamic sea ice model is used to study global climate on centennial, and longer, timescales. The model is interpreted to represent the effect of the global ocean, rather than the Atlantic, as is commonly done. It is forced by symmetric insolation and includes a diagnostic parameterization of the hydrologic cycle. Here the strength of the ocean's haline forcing is controlled by a parameter, which reflects the effect of river runoff. This parameter is varied in a set of experiments, which also differ by the magnitude of solar insolation. In wide ranges of the hydrologic cycle, multiple climatic equilibria exist, consisting of circulations with different degrees of asymmetry. More symmetric states have a higher global atmospheric temperature, characteristic of modern climate, whereas less symmetric states are colder and resemble glacial conditions. The maximum global atmospheric temperature difference between such states is consistent with proxy-data-derived temperature drop of about 4°C during the glacial, in contrast to EBM-only sensitivity of about 0.4°C. The mechanics of climate transitions in the model are due to amplification of the orbitally induced global heat budget changes by a major reorganization of the oceanic heat transport. In our model this reorganization is caused by the nonlinear dynamics of the ocean's THC, whose stability regime shifts subject to variable external forcing. Sea ice enhances model climate sensitivity by anchoring deep-ocean temperature to be near freezing [Kravtsov, 2000] and by affecting atmospheric temperature and land ice extent near the poles because of sea ice insulating properties.
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 Global climate transitions of the past and climate variability on multicentennial timescales are some of the most intriguing features of paleorecords. Understanding the mechanics of these phenomena can aid in climate prediction. There is evidence that global climate catastrophes, triggered by weak, orbitally induced, solar variations, are caused by the internal response of the oceanic thermohaline circulation (THC). This vertical meridional plane oceanic overturning is a major contributor to global heat and freshwater transport. Reconstruction of the THC during the last glacial maximum [e.g., Boyle and Keigwin, 1987; Duplessy et al., 1988] reveals a structure very different from that under present conditions. Such a bimodality of the ocean climate is also a feature of THC models.
 In this paper, we explore a two-dimensional (2-D) ocean's THC–1-D atmospheric energy balance-thermodynamic sea ice model as a minimal representation of the Earth's long-term climate. A simple standard parameterization of the land ice albedo feedback is also included. Our objective is to demonstrate the suitability of this model and look at the (multiple) steady states it produces in the context of global climate. Although many similar single-basin models have appeared in the literature before and, not surprisingly, produced solutions like those of our model, we find value in our interpretation of the modeled multiple equilibria. We associate these multiple states with glacial and interglacial climates, by interpreting our ocean basin as a zonally averaged sum of all oceans, and show that nonlinear sensitivity of our model to external forcing is enhanced by an order of magnitude compared to the linear EBM-only response. On the basis of these results, we revisit the original Milankovitch's hypothesis about the mechanics of the Earth climatic history.
 An example of evidence for the Earth climate variability during the past million years is found in the Vostok ice core record, which is proxy data that might reflect the changes in the atmospheric temperature typical for the North Atlantic region [e.g., Broecker et al., 1985]. There are several important features in this record. First, the dominant period of climatic variability, i.e., the average duration of cold glacial and warm interglacial events, is roughly 100 kyr. Second, the glacial portion of the proxy record is much noisier than its interglacial part; seemingly irregular events with durations less than 1000 years, called spikes [after Ghil, 1994] are evident. Such spikes are muted in or absent from the analogous record in Antarctica. Another feature of the record is the contrast between slow gradual onsets of the glacial periods and sharp, abrupt transitions to interglacial periods.
Milankovitch  suggested that changes in the eccentricity of the Earth's orbit affect the amount and distribution of incident solar radiation and cause global climate transitions. However, experiments with atmosphere-only energy balance models (EBMs) failed to produce a significant response to steady and time-dependent insolation changes of a reasonable amplitude [e.g., North et al., 1981]. Therefore a number of scenarios involving land ice dynamics coupled to other components of the climate system, which produce intrinsic oscillations of the climate, have been suggested [e.g., Ghil, 1994; Gildor and Tziperman, 2000, 2001]. In such models subjected to Milankovitch forcing, the internal oscillation, whose period is determined by nonlinear dynamics, phase locks to the eccentricity cycle.
 Our objective is to suggest a different scenario of climatic variability, which involves centrally the well known multiple steady states of the thermohaline circulation of the ocean. We show that thermohaline ocean dynamics may amplify the Earth system's direct response to the weak 100-kyr solar variations and produce global temperature changes between glacial and interglacial periods consistent with observations.
1.2.2. Climate at the Onset and During the Last Glaciation
 In this section we discuss studies of the inferred Earth climate during the last glaciation that started at about 115 kyears BP and achieved its maximum amplitude at 21 kyears BP, the so-called Last Glacial Maximum (LGM). Such studies have proceeded mainly in two directions: (i) extracting the information about physical characteristics of climate such as atmospheric temperature, oceanic temperature and salinity, land ice volume and others from various proxy data, and (ii) global general circulation (GCM) modeling of climate subject to past values of the external forcings.
22.214.171.124. Atmospheric and Ocean Surface Characteristics
 The glacial climate is characterized by significantly advanced land ice cover in both hemispheres and atmospheric temperatures of roughly 4°–7° colder than at present. Because of colder atmospheric temperature, the atmospheric moisture capacity decreased and the strength of the hydrologic cycle is thought to be reduced [Yung et al., 1996]. Modeling studies show the reduction in global precipitation of about 10–15% [Khodri et al., 2001; Kitoh et al., 2001; Kim et al., 2003], consistent with 10% decrease in global relative humidity compared to present values [Bush and Philander, 1999]. However, the geographical redistribution of the precipitation is nontrivial, with increased rates of precipitation in some regions, such as the USA and the Mediterranean [Kim et al., 2003], and the Indonesian Archipelago, and a much drier Western Pacific [Bush and Philander, 1999]. Thus the oceanic haline forcing's redistribution is also likely to be nontrivial and manifests itself through sea surface salinity signatures that are strongly affected not only by local precipitation, but also by river runoff [Kim et al., 2003]. For example, a relatively low salinity, compared to modern values, has been reconstructed along Canadian and Scandinavian margins, likely because of the meltwater supply by the surrounding ice sheets, by De Vernal et al. .
126.96.36.199. THC Changes
 The changes in thermal and haline forcing of the ocean are accompanied by the regime shift of the THC. In the Atlantic ocean, North Atlantic Deep Water formation site is shifted southward, deep convection is reduced, and the overturning becomes confined to the Northern Hemisphere, while the convection and deep-water formation are increased in the Southern Ocean, with Glacial Antarctic Bottom Water occupying most of the Atlantic ocean's abyss [e.g., Boyle and Keigwin, 1987; Duplessy et al., 1988; Lynch-Stieglitz et al., 1999]. These are also the features of modeled LGM climate of Khodri et al. . Fichefet et al.  estimate the reduction of the glacial NADW formation to be by about 40% compared to present-day values. Kim et al.  detect a 30% decrease in poleward heat transport in Atlantic and 40% increase in poleward heat transport in the Southern Ocean, consistent with changes in the meridional overturning.
 When used in coupled models as boundary conditions, changes in the radiative forcing and orography due to orbital and ice sheet variations explain the leading-order features of past climate change, but significant quantitative effects emerge because of inclusion of oceanic and land surface feedbacks [Kohfeld and Harrison, 2000]. Most importantly, these feedbacks might amplify the response of the system to weak solar variation that trigger glacial-to-interglacial transitions [e.g., Khodri et al., 2001]. These authors tested the hypothesis that sea surface temperature (SST) conditions that arose, presumably, because of changes in the Atlantic Ocean THC just prior to the last glaciation were instrumental in that climate transition [Cortijo et al., 1999]. They show in a global coupled ocean-atmosphere model that meridional gradient of SST was substantially enhanced before the onset of glaciation, with very cold poles and slightly warmer tropics and equatorial zones. This resulted in their model in the enhanced sea ice cover in the Northern North Atlantic, which further amplified the cooling, and weakening of the THC there. Oceanic meridional heat transport reduction was partially compensated by the increased atmospheric poleward latent heat transport, carrying the moisture to the northern latitudes and feeding the growth of the glaciers.
 The analysis of similar feedback was performed in a recent papers by Kim et al. [2002, 2003]. A coupled ocean-atmosphere GCM has been forced here with glacial time external forcing. After rapid adjustment during roughly the first 100 years of the experiment [Kim et al., 2002], the system gradually equilibrated in a glacial state, which was much colder than the corresponding state in the experiment with a mixed layer ocean. The difference is clearly attributable to the influence of oceanic feedbacks [Kim et al., 2003]. Thus feedbacks associated with changes in vegetation and ocean circulation might significantly affect the sensitivity of the climate system to the external forcing and lead to global climate transitions.
1.2.3. Idealized Modeling of Global Climate
188.8.131.52. Role of Boundary Conditions
 Multimodality of the oceanic circulation is an intrinsic property of a wide range of ocean-only models, from the simplest highly truncated box models [Stommel, 1961], to zonally averaged THC models, to idealized 3-D models [Marotzke, 1990; Marotzke and Willebrand, 1991; Weaver and Hughes, 1994], and finally to global GCMs [e.g., Moore and Reason, 1993]. However, the assumption of a fixed, or nearly fixed, atmospheric temperature and hydrologic cycle, used in the above ocean-only studies, eliminates potentially important ocean-atmosphere interactions that can influence the stability of the oceanic circulation. There is evidence that inclusion of atmospheric feedbacks enhances climate stability [e.g., Manabe et al., 1994]. Therefore Marotzke  suggested the use of the so-called coupled process models (such as that studied by Nakamura et al.  in a box model context), which modify the fixed atmosphere boundary conditions to implicitly include these feedbacks. Such a modification is essential for global climate modeling, as, in particular, there is evidence for significant atmospheric changes during the past.
 Of a particular interest are the effects of sea ice on model climate. Sea ice components have routinely been included in global OAGCMs. However, these models are extremely complicated and their interpretation is thus subtle. Process models, like those studied by Willmott and Mysak , Yang and Neelin [1993, 1997], Lenderink and Haarsma , Lohmann and Gerdes , and Jayne and Marotzke  can be helpful to illuminate the role of the sea ice in determining climate. All these studies used a simple, purely thermodynamic sea ice model to analyze possible polar effects on global characteristics of the ocean and atmosphere. Gildor and Tziperman [2000, 2001] studied a simple box model of the Earth's global climate, where the polar hydrologic cycle was strongly affected by sea ice. They obtained a 100-kyr nonlinear relaxation oscillation, with cold phase large sea ice extent inhibiting further growth of the land glaciers and triggering the onset of the interglacial.
Ganopolski et al.  considered a global ocean-atmosphere-land-sea ice model of intermediate complexity. Among other things, they concluded that the interaction of sea ice with the oceanic circulation was of a global significance for their model climate. Expansions and contractions of the sea ice cover subject to changes in oceanic overturning induced reorganizations in the atmosphere, leading to substantial response of the global atmospheric temperature. The main role of sea ice in this scenario was due to its high albedo.
Kravtsov  argued that the inclusion of sea ice in the present model destabilizes climate to hydrologic cycle perturbations because of anchoring the deep oceanic temperature to be near freezing as a result of the phase transition. On the other hand, in ranges of parameters he explored, the insulating effect of sea ice was not important for global climate stability. However, the insulating effect has been shown to lead to colder polar surface temperatures compared to the case where sea ice has been artificially suppressed. These “global versus local” roles of various relevant sea ice feedbacks have been explored in detail by Kravtsov .
1.3. This Paper
 The present work expands the process studies discussed above by comparing our box model climatologies with present and paleoclimates and considering the sensitivity of these model states to the presence of land ice albedo feedback. The explanations offered here for glacial-interglacial formation and maintenance differs significantly from those discussed elsewhere.
 The manuscript is organized as follows. In section 2 we briefly describe and discuss the model (full model formulation is given in the appendix). The description and interpretation of the reference steady states are given in section 3. In section 4, we explore in detail the sensitivity of the model to relevant parameters and parameterizations. Section 5 summarizes and expands our discussion to propose a plausible explanation for the paleoclimatic behavior.
2. The Model
 Our model ocean basin extends from pole to pole and occupies fw = 1/3 of the globe; the rest is land. The atmosphere overlies the ocean and the land. The ocean model is a widely used zonally averaged 2-D THC model. We will interpret our single-basin ocean model as that representing the effect of the global ocean on the climate of the Earth. In present paper, the main oceanic effect is due to the THC heat transport. In the present-day Northern Hemisphere, the contributions of the Atlantic and Pacific oceans to the global meridional heat transport are comparable, with the former dominated by the THC, and the latter by the wind-driven circulation heat transports. It is difficult to consistently include the parameterization of the wind-driven heat transport in zonally averaged model like ours. The choice of oceanic fraction to be fw = 1/3 of the globe (roughly twice the size of the Atlantic ocean) is thus dictated by the necessity to quantitatively capture the relative amounts of heat transported to the pole by oceans and atmosphere. Given an idealized geometry and physics in our model, this choice seems to be appropriate despite the apparent, factor of two, difference between real oceanic fraction of roughly 2/3 and the value of fw = 1/3 in the model.
 The zonally averaged, 1-D atmospheric EBM is also standard. As in many similar studies, this configuration is complemented by a 1-D thermodynamic sea ice model. Land surfaces provide an insulating boundary condition to the atmosphere, while the heat exchange between the atmosphere, ocean and sea ice is governed by the bulk laws.
 Since the model is traditional, we only list here those parts of the formulation that are referenced in the later analyses. The complete model formulation is given in the appendix.
2.1.1. Albedo and Insolation
 The system albedo, a, over the ocean-ice surface is given by
where sign(h) = 1 for positive sea ice thickness h, sign(0) = 0 for open waters; a0 = 0.316, a2 = 0.146, δ = 0.186 [Wang and Stone, 1980], and x is sine of the latitude, used as a horizontal coordinate in our model. Land ice is assumed to be present wherever Ta < −10°C [cf. North et al., 1981] and influences the climate system's dynamics via its high albedo, which is parameterized in the same form as the sea ice albedo, i.e.,
In the standard experiment discussed in section 3, the land ice albedo effect is suppressed.
 The simplified formula for time-averaged solar radiation flux at the top of the atmosphere Q is taken from North :
The atmosphere is assumed to be transparent to the short-wave radiation, so the net short-wave flux reaching the Earth's surface is given by
Traditional values for the insolation parameters are Q0 = 1355 W m−2, Q2 = −0.482 [North, 1975], although we will explore the sensitivity of our model to their variations (see section 4). Note that changes in these parameters are thought to have triggered global climate transitions in the past. In these sensitivity experiments, we include land ice and use a higher value of the albedo jump at the ice edge, δ = 0.3, which gives a reasonable value of polar albedo of about 0.8. The values of solar parameters we use there are Q0 = 1360, 1365, 1370 W m−2, and Q2 = −0.482, −0.5 [North et al., 1981].
2.1.2. Eddy Parameterizations
 The vertically integrated heat transport in the atmosphere is given by
 Here Hsen is sensible eddy heat transport, Hlat latent eddy heat transport, qs the specific humidity and C1, C2 constants chosen to fit the observed longitudinally averaged atmospheric eddy heat fluxes based on the observed meridional atmospheric temperature profile.
is the Clapeyron-Clausius equation for the saturation specific humidity of air at temperature T and ρa = 1.27 kg m−3 is the air density.
 Transports by the mean meridional circulation are not included in the model, a simplification typical of such studies. To fit observations, the standard values of C1 and C2 are chosen to be C1 = 3.7 × 106 W m−1 °C−1 and C2 = 2.3 × 109 W m−1 [cf. Rahmstorf and Willebrand, 1995]. Finally, since Hsen is determined as the difference between total and latent heat transports (see equations (4)()–(6)), care must be taken to ensure Hsen is directed down the atmospheric temperature gradient. If this is not the case, Hsen is set to zero and Hlat = Hd.
 In some sensitivity experiments (section 4), we also consider variations in C2; that is, we make C2 depend on the atmospheric temperature gradient:
in the Northern Hemisphere and
in the Southern Hemisphere, with δT = 56°C. Using equator-to-pole temperature difference instead of the local value of the atmospheric temperature gradient in the formula for ensures the same qualitative latitudinal dependence of the latent heat transport, making it suitable for a direct comparison with our standard model. In other sensitivity experiments, we use an atmosphere-only model with the ocean fraction reduced to zero. To compensate for the absence of the oceanic heat transport, C1 is increased up to C1 = 4.7 × 106 W m−1 °C−1. This value gives reasonable global atmospheric temperatures and land ice edge position compared to the full coupled model and observations.
2.1.3. Hydrologic Cycle
 For the hydrologic cycle, we assume no storage of moisture in the atmosphere or on land, and land evaporation is neglected [cf. Marotzke and Stone, 1995; Saravanan and McWilliams, 1995]. Moisture can be transported meridionally by means of atmospheric fluxes and rivers on land:
where L = 2.5 × 106 J kg−1 is the latent heat of vaporization of water, and ρo = 1000 kg m−3 is the reference water density. We assume for simplicity that river transport is proportional to atmospheric moisture transport at all latitudes, i.e.,
where At is the factor related to the size of the catchment basin over land draining into the ocean (the notation At, “Atlantic factor,” is taken from Nakamura et al. ). For example, with fw = 1/6 (representative of the Atlantic ocean) and At = 3, Mrivers = −(1/2) Matmosphere, implying half the poleward atmospheric transport integrated over latitude circle returns equatorward via rivers. Obviously, the net poleward moisture transport is then half of Matmosphere. If At = fw−1 = 6, then all freshwater carried to the poles by the atmosphere enters the ocean at the location of precipitation; that is, the meridional river transport is zero. At = 1 corresponds to the situation where the atmospheric poleward moisture transport over land is exactly compensated by equatorward river flux, and At = 0 implies no freshwater forcing of the ocean at all (poleward moisture transport by the atmosphere is exactly compensated by the equatorward river flux). The observations of Broecker et al.  suggest that the Atlantic Ocean catchment basin is such that the net haline forcing of the Atlantic exceeds the zonally averaged values of the atmospheric water vapor transport divergence by a factor of 2 to 4. So, along with fw = 1/6 (typical of the Atlantic), the value of At = 3 leads to both reasonable values of oceanic haline forcing and a reasonable structure of river transport.
 If we use fw = 1/3 to model globally averaged (all oceans) meridional circulation, At = 3 corresponds to the case of no river transport. The values of At exceeding this give rise to poleward river transport. In reality, average river transport is equatorward, so in the regime of strong haline forcing our hydrologic cycle scheme breaks down: either net oceanic haline forcing or the global river transport are not consistent with observations. Thus we will use the values of At < 3 in our experiments.
 The parameter At is, in fact, the main controlling parameter in this study. This parameter is not meant to substitute for all the complexity of the real freshwater cycle, but rather chosen as one of the simplest ways to include the river transports. Later on, we will refer to situations with large At as to those corresponding to “strong hydrologic cycle.” However, it should be realized that this terminology is applied to the ocean's effective haline forcing, so that “drier” glacial conditions (due to decreased temperature and specific humidity) might lead to stronger oceanic freshwater forcing despite there is less moisture available for precipitation. This can be caused, for example, by cardinal changes in river pathways (see section 1.2.2).
 The net oceanic haline forcing is
where aE = 6400 km is the radius of the Earth. Note that positive Mw implies the northward flux. Equation (11) guarantees the exact conservation of freshwater in our model.
2.2. Model Choices and Interpretations
 As the oceanic momentum equation is diagnostic in our zonally averaged model, the temporal evolution depends directly on the heat and salt transport equations. Temperature and salinity combine to determine density and therefore the overturning. On the other hand, advection changes the model's temperature and salinity distributions. This principal nonlinearity is essential for the model's behavior, and leads to multiple equilibria. Horizontal and vertical diffusion and convective adjustment are also included in the model. The horizontal diffusion can be thought of as a parameterization of the wind-driven gyres [cf. Winton, 1997]. Deep oceanic convection is essential for climate modeling, because it yields simultaneously reasonable values for both meridional overturning and oceanic heat transport.
 The oceanic model is coupled to a 1-D diffusive atmosphere with a diagnostic land ice albedo parameterization and a simple representation of the hydrologic cycle. The latter is perhaps the most physically questionable parameterization within the model. Partly for this reason, the coefficient determining the strength of atmospheric freshwater flux is used as a model-controlling parameter; that is, it will be varied, and the response of modeled climate to these variations will be explored [see Kravtsov, 2000]. The other, perhaps more important motivation for such sensitivity tests is that the existence and stability of model's multiple equilibria turn out to be primarily dependent on the strength of the atmosphere-land hydrologic cycle.
 Importantly, we interpret the single ocean basin in our model as a zonally weighted sum of all the oceans, so that, say, modeled oceanic heat transport should be compared with the net observed oceanic heat transport. The same applies to oceanic circulation (mass transports). For example, present-day thermohaline circulation can be characterized as the so-called conveyor belt [Gordon, 1986]. NADW enters the Indian and Pacific oceans via the ACC, upwells through the main thermocline and returns to the Atlantic ocean as a northward near-surface flow. Although the overturning in each of the basins is asymmetric, the globally averaged oceanic heat transport by overturning is roughly symmetric about the equator. Thus we are motivated to interpret our symmetric equilibrium as representative of modern conditions. This differs from many other studies, where antisymmetric equilibria are interpreted as corresponding to modern climate.
 Although we prefer our global interpretation, the more standard, single Atlantic ocean basin meridional overturning interpretation [e.g., Saravanan and McWilliams, 1995] may also be used. Remember, however, that our model's ocean has a wider longitudinal extent compared to the real Atlantic. Further discussion of the model is given by Kravtsov .
 We now discuss as a reference the equilibrium states corresponding to At = 1.9. The asymmetric state appears in Figures 1a–1d, and the symmetric state in Figures 1e–1h. Consider first the asymmetric state. Oceanic temperature (a), salinity (b), density (c) and overturning (d) are plotted. Convection regions are denoted by circles. A standard way of treating zonally averaged single-basin THC models is to compare climates they produce with the zonally averaged structure of the Atlantic Ocean [e.g., Levitus, 1982]. For direct comparison with model output, we replot the observed temperature and salinity fields on the basis of Levitus climatology in Figure 2. The Atlantic Ocean temperature distribution appears in panel (a), and salinity in panel (b). Panels (c) and (d) show the globally averaged oceanic temperature and salinity, respectively. Saravanan and McWilliams , with a similar model, discuss qualitative and quantitative comparisons between dynamic and thermodynamic properties of their modeled ocean and the real Atlantic. Our model also possesses a reasonable qualitative correspondence to the observed global climate, although our model has been tuned to reasonable values for the net world ocean heat transport. Sea ice was not included by Saravanan and McWilliams . Our model's sea ice (Figures 3a and 3b) has a realistic extent [e.g., Leppäranta, 1993; Gloersen et al., 1992], but the sea ice thickness is greatly exaggerated due, in part, to the absence of seasonal cycle. In addition, the thickness of Southern Hemisphere sea ice cover is bound to be overestimated, since our ocean basin extends all the way to the South Pole.
 From temperature and velocity, the net oceanic meridional heat transport can be computed (Figure 4). This total transport consists of an advective transport by the thermohaline overturning, and a diffusive transport; the latter thought of as a parameterization of the wind-driven gyres. Both transports are negligible under sea ice. Observations at 24°N show that total poleward heat transport in the Atlantic is 1.2 ± 0.3 PW [Hall and Bryden, 1982] and in the Pacific 0.76 ± 0.3 PW [Bryden et al., 1991]. The implied global oceanic heat transport value of 1.96 ± 0.3 PW is consistent with a recent, but lower, estimate of 1.5 ± 0.3 PW by Macdonald and Wunsch . Wang et al.  estimate the portion of the oceanic heat transport due to wind effects to be at most 25% of the total (<0.3 PW) for the North Atlantic, and 0.5–0.73 PW for the Pacific.
 The model's oceanic meridional advective and diffusive heat transport for the asymmetric climate are presented in Figure 4a. The values in the Northern Hemisphere are consistent with observational estimates of Bryden and collaborators for the total global oceanic heat transport [see also Vonder Haar and Oort, 1973; Macdonald and Wunsch, 1996]. The model's transport in the Northern Hemisphere is dominated by the overturning. The situation is different in the Southern Hemisphere, where diffusive transport dominates.
Stocker et al.  first pointed out that zonal averaging of present thermohaline circulation over the world ocean results in a less asymmetric structure because of the compensating influences of the Indian and Pacific oceans. In view of this we will refer to symmetric modes as to those representing current climate. As global OGCM studies have shown [Manabe and Stouffer, 1994; Gent et al., 1998], the asymmetries in the global zonally averaged net mass transport by the ocean may still be fairly large. This notion is also consistent with MacDonald and Wunsch . Still, our model is a metaphor for the ways by which heat is redistributed over the globe, which primarily motivates our interpretation of the symmetric model climates to represent modern conditions.
3.2.2. Asymmetric Mode
 There is evidence that global thermohaline circulation during glacial periods was more strongly asymmetric, than its modern counterpart. Indeed, the asymmetric mode can then be thought of as the circulation with an intensified sinking at one of the poles in either Atlantic or Pacific ocean, or in both [Hughes and Weaver, 1994; Rahmstorf and Willebrand, 1995]. Northern sinking states are not observed in the paleoclimate records of recent glacial and interglacial periods [e.g., Keigwin, 1987]. A strong bias against such states is also detected in the models [Hughes and Weaver, 1994]. Conversely, southern sinking states are possible. We argue that the asymmetric mode in our model bears some qualitative resemblance with recent glacial climate, where North Atlantic deep water formation was reduced and the deep ocean was filled with very cold (near freezing) water originating from the Antarctic [Duplessy et al., 1988; Boyle, 1990; Shrag et al., 1996]. An increase in the North Atlantic Intermediate Water formation during glacials has also been inferred [e.g., Duplessy et al., 1988; Duplessy and Labeyrie, 1989]. A similar feature appears in Figures 1c and 1g, where a clear increase in the thickness of the 0.002–0.003 density layer is present in the asymmetric climate. This water has a low-salinity signature (Figure 1b). Another piece of evidence for asymmetric climate during LGM has been provided by Billups and Schrag , who compiled planktonic foraminiferal oxygen isotope values from the tropical-to-subtropical Atlantic and Pacific and interpreted them in terms of meridional density gradients. They have found interhemispheric asymmetry manifested in steeper-than-today cross-equatorial density gradients in both oceans, consistent with thermocline water formation farther south in the Atlantic, and a reduced northward moisture transport in the Pacific. The changes in the THC structure during LGM discussed above have also been successfully simulated by global coupled OAGCMs (see section 1.2.2).
3.3. Symmetric Mode as a Representation of Modern Climate
 The thermohaline structure of the symmetric mode (Figures 1e–1f) should be compared with the Levitus  zonally averaged global values (Figures 2c and 2d). Sea ice distribution is depicted in Figures 3c and 3d, meridional oceanic heat transport estimates are given in Figure 4b, and the temperature distribution at the underlying surface (i.e., ocean or sea ice), as well as atmospheric temperature distribution for the symmetric reference climate, are plotted in Figure 6b. The degree of correspondence between the modeled and observed symmetric states is quite good and like that found between the modeled and observed, asymmetric, Atlantic-only climates.
 These points support the interpretation of the symmetric mode as present-day-like and the asymmetric mode as corresponding to glacial climate. We will use this interpretation later. There is thus a major difference with the Atlantic-only interpretation, where the asymmetric state is associated with modern climate.
3.4. Differences Between Symmetric and Asymmetric Modes: Paleoclimatic Perspective
 We now compare the reference states with available paleobservations, starting with atmospheric structure.
 Globally averaged atmospheric temperatures for the two reference climates are almost equal (13.99°C for the asymmetric mode and 14.06°C for the symmetric mode). This is due to the neglect of the land ice and too low a value of the albedo jump at the ice edge in this run (see section 4). Simulations of Ganopolski et al.  using a more complete “global” ocean-atmosphere-land-sea ice model show that prescribing different continental ice sheet distributions, a lower solar constant, and a reduced atmospheric CO2 amount resulted in a significant decrease of the global atmospheric temperature, the major part of which was not due to oceanic changes. We will discuss this point in some more detail below, noticing now that it does not contradict our claim of the ocean driving climate transitions [cf. Broecker, 1997].
 Our atmospheric temperature profiles for the two reference states (Figures 6a and 6b) are similar near the equator; the polar differences are about 3°C. If the southern sinking state is interpreted as a glacial climate representation, then very cold temperatures are expected in the Northern Hemisphere, consistent with paleorecords. According to our model results, the temperature of the glacial Antarctic should have been larger than the interglacial values there. Some evidence of such a behavior on centennial timescales during the most recent glacial-to-interglacial transition was presented by Broecker , although longer paleorecords [e.g., Broecker et al., 1985] show an Antarctic temperature signal of a magnitude similar to that of the “northern” signal on the 10,000–100,000-year timescale. This apparent contradiction will be discussed in more detail below (see section 4.2).
 Finally, we discuss another substantial difference between our results and those of Ganopolski et al. . An interesting comparison was made between their “full” coupled paleorun, and the one where the interior oceanic heat transport was prescribed from modern data (and thus oceanic feedbacks were disabled), with the ocean represented by a constant 50-m-deep slab. Global cooling for such a model was on average 30% less than in the “full” run, with even larger discrepancies in the Northern Hemisphere. This was argued by the authors to be due to the effect of oceanic circulation changes on sea ice. In contrast, our model shows no significant changes in the atmospheric temperature due to the sea ice albedo effect, despite the fact that sea ice cover advanced considerably. This suggests that it is not the sea ice albedo effect directly that determines the amplitude of the global atmospheric temperature change.
3.4.2. Ocean-Sea Ice Differences
 We now compare the oceanic structures of the symmetric mode and the asymmetric “southern sinking” state. The asymmetric circulation results in a reduced oceanic poleward heat transport in Northern Hemisphere, increased transport in the Southern Hemisphere (Figure 4), and the sea ice edge moves farther southward (Figures 3b and 3d). Most of the abyss is occupied by very cold (near freezing) water, originating near the South Pole. The salinity of this water is close to a basin mean value. Similar glacial characteristics have been obtained in a coupled GCM simulation by Kim et al. . This picture is also consistent with paleo-derived data, which showed that during the LGM North Atlantic deep water formation was reduced and the deep ocean was filled with very cold (near freezing) water originating from the Antarctic [Duplessy et al., 1988; Boyle, 1990; Shrag et al., 1996]. An increase in the North Atlantic Intermediate Water formation during glacials has also been inferred [e.g., Duplessy et al., 1988; Duplessy and Labeyrie, 1989], which is evident in Figures 1c and 1g as an increase in the thickness of the 0.002–0.003 density layer for the asymmetric climate. Thus the oceanic changes from the symmetric to the asymmetric mode are quite consistent with those between the interglacial and glacial climate, as derived from GCMs and paleo-observations.
 Just beyond the Northern Hemisphere sea ice edge, because of cold air transport off the ice pack, the oceanic heat loss is very strong [cf. Lohmann and Gerdes, 1998; Schiller et al., 1997]. Thus heat tends to be extracted from a very deep oceanic layer and intense sinking here is accompanied by convection. In contrast, the equilibrium heat flux from ocean to sea ice must necessarily be equal to conductive heat flux through sea ice; thus it is very small and can easily be balanced by very weak advective and diffusive ocean fluxes; that is, convection under sea ice is suppressed. It is shown in the analysis of linear and nonlinear stability of our model climates [Kravtsov, 1998, 2000] that the detailed high-latitude structure of the oceanic freshwater forcing is generally unimportant for our model behavior, nor does it affect much the steady distribution of convection in our model. Note that Ganopolski et al.  associate oceanic climatic roles primarily with changes in the location of major convection sites [see also Broecker, 1997]. In contrast, we argue that, consistent with our global interpretation, the large-scale advective effects in the ocean can drive climate transitions. Local polar changes may possibly be secondary effects of the global advective oceanic climate catastrophes [see also Kravtsov, 1998].
 It appears that changes in the convective activity for different model climates are determined by differing advective balances. For example, we can see that only relatively shallow convection occurs in the open ocean region close to the sea ice edge. This is due to a fairly low salinity of the water circulating in the smaller overturning cell (Figure 1). The temperatures of the northern abyssal and upper waters are very close. Therefore the convection in the Northern Hemisphere cannot penetrate much deeper than the boundary of the southern deep salty water blob. Note again that the sharp drop in the precipitation near the ice edge (a consequence of the abrupt atmospheric temperature profile near the sea ice edge and the diagnostic formula for the atmospheric freshwater flux) cannot be the reason for the lower salinity of smaller cell. The actual reason lies in the fact that this secondary circulation contacts the surface in the region of net precipitation and is thus shielded from high equatorial evaporation influence. The causal connection between deep convection and global sinking in the ocean is unclear [e.g., Rahmstorf, 1995a]. In our model the role of convection is only auxiliary; that is, the convective pattern adjusts to long-term climate changes, but does not drive them [Kravtsov, 1998]. In summary, the differences in the advective temperature and salinity balances constitute the essence of our model multiple equilibria and we argue it possible to draw corresponding parallels with multiplicity of the Earth's climates inferred from paleodata.
4. Model Sensitivity to Insolation and Hydrologic Cycle
 In these experiments, we include land ice albedo and use a higher value of the albedo jump at the ice edge of δ = 0.3 (rather than δ = 0.186), as described in section 2.1. Using this value of δ gives a reasonable polar albedo of about 0.8. We also vary the insolation parameters Q0 and Q2 and find possible steady states of the system for different strengths of the hydrologic cycle, controlled by the parameter At. Since we have increased the albedo of the system, we generally use higher values of the solar constant Q0 to produce reasonable values of the global atmospheric temperature. Conceptually, changes in Q0 correspond to the effect of the Earth's orbit variations because of eccentricity, and changes in Q2 correspond to variations because of obliquity. These are the changes that are thought to have triggered glacial-interglacial transitions in the Earth's climate.
Kravtsov  showed that high vertical resolution is not essential for the qualitative oceanic behavior of our model. He constructed a simpler two-layer model that was shown to have the same bifurcation properties as the full 2-D ocean model. This model, however, has the same high horizontal resolution as the full model to naturally resolve the sea ice structure. In this section, we will experiment with the simplified model and pay a particular attention to the changes in global atmospheric temperature, land ice, and sea ice extent. All steady states were obtained by a direct time integration of the coupled model.
4.1. Experiments With Weak Dependence of the Hydrologic Cycle on Meridional Temperature Gradient
 The summary of the experiments with the coupled model, where the atmospheric moisture transport is proportional to dqs/dx is given in Table 1. The values for the symmetric, or near-symmetric, climates are indicated with a superscript b. For a fixed insolation, the results are conceptually similar to those obtained by Kravtsov : at sufficiently strong hydrologic cycle the symmetric/nearly symmetric circulation becomes unstable and strongly asymmetric circulations arise. Interestingly, we found multiple asymmetric states within the range of At, where the symmetric circulation is unstable (values in brackets in Table 1). Generally, the more asymmetric the state is, the colder is the global atmospheric temperature, consistent with our interpretation of the asymmetric climates as corresponding to glacial conditions.
Table 1. Steady State Global Atmospheric Temperature Ta and the Latitudes of Sea Ice (λSI,S, in the Southern Hemisphere; λSI,N, in the Northern Hemisphere) and Land Ice (λLI,S, in the Southern Hemisphere; λLI,N, in the Northern Hemisphere) Edges as Functions of Hydrologic Cycle Parameter At and Insolation Parameters Q0 and Q2a
In case multiple equilibria are found, the values corresponding to an alternative steady state are given in parentheses Meridional moisture transport in the atmosphere ∼ dqs/dx.
 The characteristic change in global atmospheric temperature between the symmetric and the most asymmetric states is a couple of degrees, much larger than that in the standard run with small albedo and no land ice discussed in section 3. The asymmetric states are characterized by (1) an advanced land ice and sea ice cover and very cold temperatures (not shown) in the Northern Hemisphere, (2) slightly colder (1–2°C) equatorial temperatures (not shown), and (3) a retreated land ice, sea ice cover and warmer temperatures (not shown) in the Southern Hemisphere.
4.2.1. Unrealistic Behavior in the Southern Hemisphere
 The latter property contradicts very low frequency behavior observed in paleorecords, as mentioned in section 3.4. Similar Southern Hemisphere behavior was documented by Gildor and Tziperman . They have proposed a number of possible explanations for this discrepancy, one of which involved the lack of explicit representation of the Southern Ocean dynamics, which takes into account wind-driven upwelling, in the model. Kim et al.  described the global coupled model simulation of the climate during the LGM. It was characterized by an asymmetric state like that in our model, with the 40% decrease in the poleward heat transport in the North Atlantic, and a similar increase in the Southern Ocean. This also resulted in their model in a reduced sea ice cover in the Southern Hemisphere, accompanied by the decreased zonal winds there. Observations of Moore et al.  suggest expanded Southern Hemisphere sea ice cover and windier conditions, which might mean that the two properties are directly connected and responsible for the unrealistic behavior by Kim et al.  and Gildor and Tziperman  and in our model. Another possible explanation might involve global sea level decrease due to growth of the glaciers, resulting in a larger land fraction in Antarctica and, possibly, to colder atmospheric temperatures there. Note that our ocean extends all the way to the South Pole. Introducing Antarctic land mass will inevitably produce a cold bias in our Southern Ocean, which, along with sea level–land fraction feedback might lead to improved model behavior.
4.2.2. Roles of Sea Ice Albedo, Insulation, and Phase Transition Effects
 The first two features of our model's glacial climate are, however, consistent with the results of Ganopolski et al. . These authors attributed their model's very low northern region temperatures during glacial period to the sea ice albedo effect. Additional experimentation with the sea ice albedo effect suppressed in our model produced the results similar to those in Table 1 (not shown). Thus the sea ice albedo effect is secondary. The major part of the polar temperatures drop in the asymmetric state in our model is due to sea ice insulation effect, which conditions the low atmospheric temperatures and allows the land ice to grow. If the sea ice is artificially suppressed, warmer polar conditions arise (not shown) that prevent formation of a land ice. Note, however, that the influence of the insulation effect in our model is local to the poles, while main global influence of the sea ice is due to its phase transition property that affects the stability of the THC in our model, leading to increased model sensitivity to the perturbations of the hydrologic cycle [see Kravtsov, 2000].
 For a given Q0, variations in Q2 lead to a relatively minor effect, whereas the effect of changing Q0 on the atmospheric temperature is quite large (see below). The value of Q0 = 1370 W m−2 corresponds to the steady states resembling the modern conditions (for sufficiently low At).
4.3. Experiments With Strong Dependence of the Hydrologic Cycle on Meridional Temperature Gradient
Table 2 is a summary of the same experiments as those described above, but with atmospheric moisture transport proportional to (dTa/dx)3dqs/dx (see section 2.1). These produce qualitatively similar results, but the sensitivity of the atmospheric temperature is increased even more (this is not surprising given sharper dependence of the moisture transport on the atmospheric temperature gradient). Note that in this case, the nearly symmetric and strongly asymmetric states often coexist at large values of At and fixed insolation parameters.
Table 2. Same as Table 1 but for Meridional Moisture Transport in the Atmosphere ∼(dTa/dx)3dqs/dxa
In case multiple equilibria are found, the values corresponding to an alternative steady state are given in parentheses Meridional moisture transport in the atmosphere ∼ dqs/dx.
 In Table 3, the analogous results from the atmosphere-only EBM (see section 2.1) are shown. They provide us with the reference sensitivity of our model to the changes in the solar forcing with THC feedbacks suppressed. Here, changing Q0 from 1370 to 1365 W m−2 results in a global temperature drop of 0.8°C and a 1.4° equatorward shift of the ice line, while Q0 changes from 1365 to 1360 W m−2 produce the shifts of 1.6°C and a 4.2°, respectively. If we associate the climate at Q0 = 1370 W m−2 with modern conditions (based on global atmospheric temperature and ice extents), then 100-kyr insolation changes would have an amplitude of about 2.5 W m−2 [North et al., 1981], which will give rise to global atmospheric temperature changes of about 0.4°C and a ∼1° shift of the equilibrium ice line, according to Table 3. These values are consistent with North et al. . If the THC and sea ice feedbacks are included, the increase in (nonlinear) sensitivity comes from the existence of the multiple equilibria. For example, at At = 3 and Q0 = 1370 W m−2, two multiple equilibria are listed in Table 2, which differ by as much as 4°C in terms of a globally mean atmospheric temperature and by a ∼15° shift in the Northern Hemisphere ice edge. Thus the sensitivity increase due to internal THC dynamics in our model can be as much as by a factor of 10 (4°C, 15° intrinsic changes versus 0.4°C, 1° directly forced changes).
Table 3. Steady State Global Atmospheric Temperature Ta (°C) and the Land-Ice-Edge Latitude λLI (°) as Functions of Insolation Parameters Q0 and Q2 in the Atmosphere-Only EBM (See Text)
Q0, W m−2
4.5. Summary of the Sensitivity Experiments
 The sensitivity tests of this section are summarized in Figure 7. Shown here in panel (a) are At dependencies of the global maximum (i.e., between the warmest possible and the coldest possible states) atmospheric temperature differences between the high and low solar constant conditions for the experiments with atmospheric moisture transport proportional to dqs/dx (see above). Solid lines and circles correspond to the change in Q0 from 1370 to 1365 W m−2 and dashed lines and crosses correspond to the change in Q0 from 1365 to 1360 W m−2. The reference sensitivities of the atmosphere-only EBM are shown by the horizontal lines. Panel (b) is analogous to panel (a), but for the experiments with atmospheric moisture transport proportional to (dTa/dx)3dqs/dx. For most of At, the model sensitivity is increased compared to that of the corresponding atmosphere-only EBM. These large differences in the atmospheric temperature are due to those between less symmetric and more symmetric oceanic states (see above). The most dramatic signal of about 4.5°C in global temperature is obtained for the change in Q0 from 1370 to 1365 W m−2 with atmospheric moisture transport proportional to (dTa/dx)3dqs/dx and At > 2. The changes in meridional heat transport between the states that correspond to the global maximum atmospheric temperature differences between the high and low solar constant conditions (Figure 7) are consistent with GCM simulations of Kim et al. . As discussed above, almost all of this signal is due to differences between the two equilibria of our model THC. This illustrates again our main point: in our coupled model THC dynamics drastically increases climate sensitivity compared to that of the atmosphere-only model.
5. Summary and Discussion
 In this study we consider a simple model of long-term (100 kyr +) global Earth climate to address the possible types of climate, their mechanics, and climate transitions. We treat the climate system as a heat engine driven by a slowly varying, latitudinally nonuniform solar energy input. The latitudinal dependence requires compensating poleward heat transports in the ocean and atmosphere. The condition of these thin oceanic and atmospheric layers constitutes the climate of the Earth.
 Despite the fact that temperature effects are normally dominant in determining the oceanic density field, the stability of ocean circulation and climate sensitivity may crucially depend on the oceanic salinity field and hence on the global hydrologic cycle [Stommel, 1961]. This is our point of view in this study. The Earth climate is considered to be mainly controlled by the oceanic thermohaline circulation. Even though the temperature torque determines the sense of this circulation, salinity is important for climate stability. Global climate transitions (even if triggered by external factors) are physically the result of fine changes in the temperature and salinity contributions to mean and perturbation oceanic heat and salt balances.
 Our model exhibits symmetric and asymmetric equilibria. We interpret more symmetric states as the modern climate. Similarly looking pictures can be derived from observations. It is thought that in glacial times, the major oceanic sinking occurred at the South Pole in both the Atlantic and Pacific oceans, North Atlantic Deep Water formation was reduced and intermediate water formation increased. The deep ocean was filled with very cold water penetrating from the south [e.g., Duplessy et al., 1988]. Therefore the more asymmetric mode is interpreted as representative of glacial conditions. To our knowledge this symmetric-asymmetric mode interpretation, which is implicit in many studies, has never been articulated.
 There is evidence that major climatic transitions were triggered by slow changes in external solar forcing. Hays et al.  have demonstrated a significant correlation between principal periods of climatic variations and those of the Earth's orbital parameters. North et al. , however, described the failure of simple atmospheric energy balance models to produce correct amplitudes for solar forcing-induced climate change, indicating inability of these models to support the hypothesis of climate transitions, directly induced by the insolation changes [Milankovitch, 1969]. This is also the case for more complete atmospheric models (see, e.g., the relevant discussion by Broecker ). We argue that this is possibly a consequence of the neglect of ocean dynamics. Changes in oceanic circulation like those observed in our model can amplify the response of the global system to external forcing variations.
 Quasi-periodic solar forcing possesses spectral peaks at roughly 20, 40, and 100 kyears, the first two peaks being much stronger the last one. A puzzling property of the climate response is the clear dominance of the 100-kyr timescale in glacial-interglacial transitions. Ghil  explains most features of the paleorecord as the result of nonlinear interaction between land ice–bedrock dynamics and the 20- and 40-kyr solar forcing. Others [Gildor and Tziperman, 2000, 2001] have proposed a scenario, where sea ice inhibition of polar evaporation was essential for initiating the transition from glacial to interglacial period. This oscillation was shown to be phase locked to the 100-kyr-period part of the Milankovitch forcing.
 Other related scenarios concern the Younger Dryas, i.e., a pronounced cold signal during the warming from the last glacial to interglacial. The duration of the event is estimated to be less than 1000 years. It is customary to interpret it as a result of the Earth's climate bimodality, i.e., a temporary return to glacial conditions because of strong meltwater flood into the North Atlantic [e.g., Broecker et al., 1985; Fairbanks, 1989; Broecker, 1997]. The event is most pronounced in the North Atlantic; no clear signal is observed in Antarctic. Such interhemispheric asymmetry is also a feature of our model's climates. In addition to the massive flood advective scenarios, there are corresponding convective scenarios [e.g., Rahmstorf, 1995b], where the direct result of the high-latitude glacial freshwater input is the local shutdown of convection leading to THC collapse and return to colder conditions.
 Here, we propose that glacial transitions result directly from the weak 100-kyr solar variations [cf. Milankovitch, 1969]. These have a truly global character, unlike 20- and 40-kyr forcings, which have a hemispherically asymmetric structure [Ghil, 1994]. Further, our scenario does not involve phase locking of an internal 100-kyr land ice oscillation [Gildor and Tziperman, 2000, 2001]. We show in our model that weak global insolation changes result in a shift of the stability regime of oceanic circulation and cause a weakening of the net oceanic poleward heat transport in the Northern Hemisphere, along with a corresponding increase in the Southern Hemisphere. This induces the Northern Hemisphere land ice advance and final onset of the cold glacial period. Oceanic THC dynamics are essential here; sensitivities of the atmosphere-only EBM to changes in the solar constant are much smaller, consistent with previous studies [e.g., North et al., 1981].
 A similar explanation of the glacial-to-interglacial transition mechanics has been put forward by Paillard . He constructed an ad hoc threshold model, in which three different climatic states are prescribed to occur depending on the values of solar forcing and total land ice volume. The states are speculated to be generated by the THC mechanics in a box model of the type used by Stommel . In such a strongly nonlinear model, very weak solar variations are able to excite climate transitions with realistic amplitude and timing, when the solar forcing crosses the thresholds associated with the three possible states. With our model that has many more degrees of freedom than the Paillard's  model and incorporates a well-defined set of dynamical features, we are able to look in greater detail at the relative roles of various physical processes that affect climate transitions. In particular, we have addressed the role of sea ice.
 Sea ice affects model's sensitivity in two ways. First, it locks the deep oceanic temperature to the freezing point because of sea ice phase transition. This destabilizes the symmetric model climate to the perturbations of the hydrologic cycle [see Kravtsov, 2000]. The resulting unstable mode has a maximum strength near the equator and equilibrates in an asymmetric circulation. The second effect is a local polar effect of insulation, which conditions the cold atmospheric temperatures near the pole and allows the land ice to grow, making atmospheric temperatures even colder because of land ice albedo effect. Sea ice albedo effect is also destabilizing in this sense, but is of a secondary quantitative importance.
 The major drawback of our model is an unrealistic underestimation of sea ice and land ice in our glacial climate Southern Hemisphere. Possible reasons for this discrepancy include the lack of explicit representation of the Southern Ocean dynamics, which takes into an account a wind-driven upwelling [Moore et al., 2000; Kim et al., 2003; Gildor and Tziperman, 2000], the absence of CO2 feedback, and, finally, neglect of sea level changes that accompany glacial transitions in our model. These effects should be included in future experiments.
 We also plan to complement this study by experiments with time-dependent Milankovitch, seasonal and white noise forcing. Indeed, the steady state description of the present paper is not enough to sustain the claim that a new mechanism for the glacial-to-interglacial transition has been established. A number of possible transient behaviors might be found. By inspection of, for example, Table 1, one can see that the difference between the virtually symmetric climates forced by low- and high-insolation levels at At = 1.6 is already a couple of degrees, although it is lower than the temperature difference arising in transitions from symmetric to asymmetric states at higher values of At. Such a preconditioning of the glacial onset might have occurred in reality [Cortijo et al., 1999; Khodri et al., 2001] during the last glacial inception (roughly 115 kyears BP). Note also, that the sensitivities shown in Figure 7 are obtained with fixed values of At. In the experiments using time-dependent forcing, one might want to allow for the fact that river runoff changed drastically through the Earth's climate history. A possible parameterization of the fully coupled hydrologic cycle can be developed, on the basis of our results, in which At increases as the global atmospheric temperatures drop, corresponding to the decreased equatorward transport of fresh water by rivers.
 The steady states in this paper were obtained by changing At parameter by a small amount and using previous At steady state as an initial condition for the subsequent run. During these experiments, we noticed an interesting asymmetry between the runs with increasing and decreasing At. The coldest phase seems to be more stable and with increasing At, it transitions directly to the warmest mode, whereas experiments with decreasing At show a more gradual transition. Such asymmetries might manifest themselves in the time-dependent forcing experiments as slow onsets of the glacials and rapid transitions to interglacials, as observed in the paleorecord.
 Preliminary results indicate that if we associate an increased equator-to-pole temperature gradient with enhanced atmospheric eddy activity and model it as a white noise forcing of our system, it excites the damped oscillatory eigenmode of the ocean, having an advective (several hundred to a thousand years) timescale [see Kravtsov, 1998]. Interaction of this eigenmode with sea ice produces large spikes, consistent with the proxy-derived atmospheric temperature in the North Atlantic region [e.g., Broecker et al., 1985]. The spikes' effect in the South Pole of the model is much less pronounced, which is also consistent with paleorecord.
 The picture of the climate history alluded to in this paper supports the Milankovitch hypothesis of the weak changes in the Earth's orbit eccentricity being directly responsible for the onset and termination of the ice ages. We also hypothesize that THC-based dynamics might explain shorter timescale events seen in the paleorecord.
Equation (A1) describes 2-D incompressible, nonrotating, hydrostatic flow in the meridional vertical plane of a stratified ocean. Rotation is implicit in the values of frictional coefficients [e.g., Marotzke et al., 1988]. A linear equation of state for the seawater is assumed. Equation (A2) defines the zonal vorticity component and equations (A3)–(A4) govern the tracers T (temperature) and S (salinity). The quantity x = sin(λ), where λ is the latitude, is used as a horizontal coordinate and z = z*/D is a nondimensional vertical coordinate. The quantity aE = 6400 km is the radius of the Earth. A rigid lid at z* = 0 and a flat bottom at z* = −D = −4000 m are assumed, J(A,B) ≡ [∂xA ∂zB − ∂xB ∂zA] is the Jacobian. The stream function ψ defines vertical (w) and generalized meridional velocities (v ≡ dx/dt) by w = (1/aE)∂xψ and v = −(1/D)∂zψ. AH and AV are horizontal and vertical eddy viscosities, kH and kV are horizontal and vertical eddy diffusivities, α = 2 × 10−4 °C−1 and β = 8 × 10−4 psu−1 are thermal and haline expansion coefficients and g = 9.82 m s−2 is the gravitational acceleration.
 The equations are finite differences and solved numerically subject to no-normal flow and free slip boundary conditions for the velocities (ψ = 0, ψzz = 0), and no-flux boundary conditions on the sides and the bottom for tracers. The boundary conditions at the ocean's surface in the ice-free regions have the form
Here ρo = 1000 kg m−3, cp = 4000 J kg−1 °C−1 are water density and heat capacity, = 35 psu is the mean ocean salinity and Fw stands for freshwater flux with downward flux (net precipitation) being positive. Hs is the oceanic heat forcing. In ice-covered regions, we have
where Tf = −1.9 °C is the freezing temperature of the sea ice and h is the sea ice thickness. In our formulation, Tf is actually the oceanic upper (62.5-m-deep) mixed layer temperature [cf. Hibler and Bryan, 1987]. The sea ice bottom temperature is held constant at Tf. Following Bryan , precipitation is assumed to penetrate through the sea ice directly into the ocean.
 The standard set of model parameters is AV = 400 m2s−1, AH = 2 × 109 m2s−1, kV = 10−4m2s−1, kH = 1000 m2s−1 for z < −1062.5 m and kH = 5000 m2s−1 for z > −1062.5 m. The larger surface value of kH is meant to model heat transport by the wind-driven gyres [cf. Winton, 1997; Mysak et al., 1993].
 An implicit vertical diffusion (IVD) scheme is used for the convective adjustment. To provide efficient mixing of statically unstable regions, kV is set to 1m2s−1.
 Short wave radiation and albedo parameterization were discussed in section 2.1. For the outgoing long wave radiation from the Earth we have
where the values of
are taken from Wang and Stone . In (lwr), Ta is atmospheric temperature in °C. With these, the net (zonally averaged) radiation forcing at the top of the atmosphere, Hnet, as a function of latitude is
 Assuming perfect longitudinal mixing in the atmosphere, the equation for atmospheric temperature Ta is
where = 273 K, Ts stands for SST or sea ice surface temperature (IST) expressed in K, ca = 1004 J kg−1 °C−1 is the air heat capacity and Ha = 8 km is the height of the atmosphere. The first term on the right-hand side of (A11) describes long wave radiation loss by the atmosphere. The atmosphere radiates both up and down; the downward flux is absorbed by the ocean. The terms proportional to the Boltzmann constant σ = 5.7 × 10−8 W K−4 describe the long wave radiation loss by the ocean or sea ice surface. The Stefan-Boltzmann formula has been linearized about . The λ term on the right-hand side of (A11) is a parameterization of the sensible and latent heat exchange between ocean and atmosphere or sea ice and atmosphere. For air-sea flux we use the value of λ = 35 W m−2°C−1 [Haney, 1971], while in the case of air-sea ice heat exchange λ = 24.2 W m−2°C−1 is used [Maykut, 1986]. H1 is the heat exchange with the land. Neglecting land heat capacity and conductivity, one can write
The meridional heat transport divergence term G is
where atmospheric eddy heat transport Hd is given by (5).
 The net heat flux to the ocean or sea ice from the atmosphere can be found as
 The sea ice thickness (h) evolution is described by
Here ρiLf = 2.72 × 108 J m−3 [Maykut, 1986] and KH = 1000 m2s−1. Hoc is computed as a sum of the heat flux into the oceanic mixed layer (whose temperature is fixed at Tf) from the underlying ocean and the contribution of the oceanic lateral heat transport. The sea ice surface temperature (IST) is determined using
where the value for ice conductivity ki ∼ 2.17 W m−1°C−1 is adopted from Semtner .
 The discussions of various aspects of the research with Dr. Jochem Marotzke were very useful. Dr. Harper Simmons helped to generate Figure 2. Ms. Jane Jimeian's support in handling software and hardware problems is gratefully acknowledged. We are also grateful to the two reviewers, whose comments greatly improved the manuscript. This research was supported by the NSF Grant OCE-9401977 and NASA Grant NAGW-3087.