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  • View in gallery

    GENESIS July surface air temperature bias over North America measured as the difference between a present-day simulation and the Legates and Willmott observational dataset. The square box refers to the region plotted in Fig. 6, and the lines of longitude refer to the transects in Fig. 7.

  • View in gallery

    ELA (solid black line) and July 0° isotherm (solid white line) simulated in the initial ice-free state and overlain on a map of the bedrock topography used in the ISM.

  • View in gallery

    Time series of ice volume and ice area in (a),(b) Canada and (c),(d) Greenland for all coupling experiments. Equivalent sea level (right axis) is corrected for isostatic loading on the lithosphere. Ice area is often referred to as accumulation area in the text because they are approximately equal during the first 10 kyr, consistent with theory (Weertman 1964). Note the change in scale of the time axis at year 10 000.

  • View in gallery

    Difference in July surface air temperature between various times throughout the f500 experiment and the initial ice-free state (CNTL). Areas covered by ice throughout the experiment are masked out.

  • View in gallery

    (a),(b) Departure of July sea level pressure and July surface winds from the initial ice-free state (CNTL) at various times throughout the f500 experiment and (c),(d) difference in July vertically integrated northward transport of sensible heat from the initial ice-free state (CNTL) at various time throughout the f500 experiment. The thick black line is zero contour and the solid (dashed) lines are positive (negative) values, contour interval 100 K m s−1.

  • View in gallery

    Scatterplot of July surface air temperature relative to the ice-free run for all climate updates averaged over a land region between the Laurentide and Cordilleran ice sheets (see Fig. 1) against mean height of the Laurentide Ice Sheet lying under anticyclonic flow. As the Laurentide Ice Sheet grows in height, the July summer temperatures increase.

  • View in gallery

    Difference in July atmospheric temperature for years (left) 1000, (right) 3000, and (right) 5000 in the high-frequency coupling experiment and the initial ice-free state in the latitude–height plane for (top) western, (middle) central, and (bottom) eastern Canada. See Fig. 1 for exact locations. Thick black line is the zero contour and solid (dashed) lines indicate positive (negative) values, contour interval 0.5 K.

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Terminating the Last Interglacial: The Role of Ice Sheet–Climate Feedbacks in a GCM Asynchronously Coupled to an Ice Sheet Model

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  • 1 Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, Ann Arbor, Michigan
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Abstract

Climatic deterioration in northeastern Canada following the last interglacial resulted in the formation and abrupt expansion of the Laurentide Ice Sheet. However, the physical mechanisms leading to rapid ice sheet expansion are not well understood. Here, the authors report on experiments using an ice sheet model asynchronously coupled to a GCM to investigate the role of ice sheet–climate feedbacks in terminating the last interglacial period. In agreement with simpler models, the experiments indicate that a specific type of ice–albedo feedback, the small ice cap instability, is the dominant process controlling rapid expansion of the Laurentide Ice Sheet. As ice elevations increase in northeastern Canada, a stationary wave forms and strengthens over the Laurentide Ice Sheet, which acts to hinder further expansion of the ice margin and reduce the effect of the small ice cap instability. The sensitivity of these feedbacks to ice topography results in a reduction in simulated ice volume when the communication interval between the GCM and ice sheet model is lengthened since this permits larger gains in ice elevation between GCM updates and biases the simulation toward a stronger stationary wave feedback. The shortest communication interval (500 yr) leads to a Laurentide ice volume of 6 × 106 km3 in 10 kyr, which is less than ice volume estimates based on the geological record but is a substantial improvement over previous GCM studies. The authors discuss potential improvements to the asynchronous coupling scheme that would more accurately resolve ice sheet–climate feedbacks, potentially leading to greater simulated ice volume.

Corresponding author address: Adam R. Herrington, Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI 48109. E-mail: adamrher@umich.edu

Abstract

Climatic deterioration in northeastern Canada following the last interglacial resulted in the formation and abrupt expansion of the Laurentide Ice Sheet. However, the physical mechanisms leading to rapid ice sheet expansion are not well understood. Here, the authors report on experiments using an ice sheet model asynchronously coupled to a GCM to investigate the role of ice sheet–climate feedbacks in terminating the last interglacial period. In agreement with simpler models, the experiments indicate that a specific type of ice–albedo feedback, the small ice cap instability, is the dominant process controlling rapid expansion of the Laurentide Ice Sheet. As ice elevations increase in northeastern Canada, a stationary wave forms and strengthens over the Laurentide Ice Sheet, which acts to hinder further expansion of the ice margin and reduce the effect of the small ice cap instability. The sensitivity of these feedbacks to ice topography results in a reduction in simulated ice volume when the communication interval between the GCM and ice sheet model is lengthened since this permits larger gains in ice elevation between GCM updates and biases the simulation toward a stronger stationary wave feedback. The shortest communication interval (500 yr) leads to a Laurentide ice volume of 6 × 106 km3 in 10 kyr, which is less than ice volume estimates based on the geological record but is a substantial improvement over previous GCM studies. The authors discuss potential improvements to the asynchronous coupling scheme that would more accurately resolve ice sheet–climate feedbacks, potentially leading to greater simulated ice volume.

Corresponding author address: Adam R. Herrington, Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI 48109. E-mail: adamrher@umich.edu

1. Introduction

Ice sheet expansion following the last interglacial period [marine isotope stage 5e, circa 130–120 (×103) years ago (ka ≡ 103 years ago)] was extremely rapid. Terrestrial and marine stratigraphic records indicate that sea level dropped by about 50 m in 10 × 103 yr (10 kyr) due primarily to the formation and advance of the Laurentide Ice Sheet in northeastern Canada (Mix 1992; Clark et al. 1993; Shackleton 2000; Cutler et al. 2003). The large sea level drop requires large, rapid gains in the accumulation area of the nucleating Laurentide Ice Sheet, which is difficult to explain by slow spreading through ice deformation (Weertman 1964; Andrews and Mahaffy 1976; Calov et al. 2009). Therefore, a large climatic cooling must have accompanied reduced summer insolation circa 120–110 ka in order to submerge large regions of northeastern Canada with perennial snow (Ives 1957; Barry et al. 1975). Although an energy balance model (EBM) (North et al. 1983; Crowley and Hyde 2008) and, more recently, Earth models of intermediate complexity (EMICs) (Wang and Mysak 2002; Kageyama et al. 2004; Calov et al. 2009) simulate the large cooling and gains in perennial snow cover over northeastern Canada at that time, general circulation models (GCMs) simulate temperatures that are too warm (see Yoshimori et al. 2002, and references therein).

EBMs owe their success in simulating glacial inception to the small ice cap instability (SICI) (North 1984). The SICI is a peculiar type of ice–albedo feedback that leads to unstable growth of ice caps into finite size ice sheets (note the term “ice cap” is used loosely here since the instability may only require the existence of a perennial snowfield, which is a precursor to ice cap formation). The SICI occurs because small ice caps act as a heat sink for surrounding regions, which leads to cooling in front of the margin and ice cap expansion. The SICI requires atmospheric heat transport to be strongly influenced by horizontal gradients in surface heating, which are large across an ice cap margin owing to the difference in albedo between ice and land. The parameterization of atmospheric heat transport in EBMs as diffusion of the surface temperature field creates very efficient heat transport across the ice margin and leads to a pronounced SICI and rapid ice cap growth.

Meteorological evidence provides some justification for this treatment of heat transport. In middle to high latitudes, surface air temperature anomalies measured at meteorological stations are well correlated over a distance of about 1200 km (Hansen and Lebedeff 1987), suggesting that horizontal transport through the atmosphere spreads local heating anomalies over a great distance, a process referred to as horizontal dampening. Although experiments have shown that horizontal dampening does occur in GCMs (North et al. 1992; Hall 2004), these models consistently produce only small ice caps in response to the cool summer orbit 116 ka (Yoshimori et al. 2002).

It is reasonable to question whether SICI is a real feature or merely a phantasm of EBMs. There are today numerous examples of stable ice cap margins around the world (e.g., Barnes Ice Cap on Baffin Island and Vatnajkoll in Iceland) that might be argued as evidence that SICI does not exist in the real world. However, the incipient Laurentide Ice Sheet does not have a modern analog and existed under conditions that were likely ideal for SICI. We speculate that the SICI only occurs under the rare conditions when an ice cap is not geographically constrained by coastlines or elevation, is sufficiently large and continental to influence regional atmospheric circulation and create large temperature gradients, and is exposed to climatically favorable conditions (such as occurred during glacial stages). Previous studies support our speculation. Crowley et al. (1994) applied the Global and Environmental and Ecological Simulation of Interactive Systems (GENESIS) GCM to the Carboniferous ice age (270 × 106 yr ago) and found that a perennial snowfield (40-km radius) expanded into a massive snowfield (3000-km radius) over the pole-centered continent of Gondwanaland after a 0.5% reduction in the solar constant (from 98.0% to 97.5% of modern). This remains the only GCM study that clearly demonstrates a SICI [however, see the study of Lee and North (1995) for potential SICI behavior in a GCM]. A SICI was also identified in the Climate-Biosphere model (CLIMBER-2) EMIC coupled to an ice sheet model (Calov et al. 2009), which incorporates a statistical–dynamical model of the atmosphere (Petoukhov et al. 2000) and therefore provides additional evidence that the SICI is not an artifact of EBMs.

GCMs resolve dynamical features including the stationary wave field that are not represented in simpler models but may influence ice sheet evolution (Oerlemans 1979). Using a simple two-layer quasigeostrophic model, Roe and Lindzen (2001) demonstrate the importance of resolving glacial anticyclones over a growing ice sheet. Glacial anticyclones create strong zonal asymmetries in the temperature field that affect ice sheet shape and size. This stationary wave response acts as a positive feedback in their model because northerly winds predominate over most of the ice sheet, due to a slight westward shift of the anticyclone with respect to the ice sheet summit (Roe and Lindzen 2001). However, no GCM study has investigated the role of this feedback in the rapid inception of the Laurentide Ice Sheet.

In this study, we present results from a GCM coupled to an ice sheet model (ISM) in order to study the feedbacks that lead to ice sheet inception in North America and Greenland. Owing to the computational expense of GCMs and the long equilibration time of ice sheets, it is not presently feasible to synchronously couple an ISM to a GCM over 1000-yr time scales. Therefore, acceleration techniques are often used to couple GCMs to ISMs, in which the GCM and ISM communicate at intervals from just a few years to 10 kyr (Ridley et al. 2005; Pollard and DeConto 2005; Pritchard et al. 2008; Vizcaino et al. 2008; Horton and Poulsen 2009). These techniques are justified by the fast response time of the atmosphere compared to ice sheets.

However, recent experiments with an EMIC suggest that simulated ice volumes decrease when the communication interval between a GCM and ISM is lengthened (Calov et al. 2009). This indicates that the response time may impose tighter restrictions on the communication interval than previously thought. In light of this, we have performed our experiments using a range of different communication intervals. In contrast to the study of Calov et al., we perform our experiments using constant radiative forcing in order to determine whether feedbacks between ice sheets and the atmosphere are affected by the communication interval. We find that simulated ice volume does decrease when the communication interval between the ISM and GCM is lengthened, because of a positive SICI feedback and a negative stationary wave feedback, both of which are sensitive to the communication interval.

2. Models

a. AGCM

The GENESIS version 3.0 atmospheric GCM consists of an Eulerian spectral dynamical core coupled to a 50-m slab ocean and a land surface model (Thompson and Pollard 1997). The slab ocean diffuses heat down the local temperature gradient, with a latitudinally varying diffusion coefficient. The atmospheric model was run at T31 horizontal resolution (3.75°) with 18 vertical sigma levels. A semi-Lagrangian transport scheme is used for water vapor.

The land surface transfer scheme (LSX) model (Pollard and Thompson 1995) runs at a finer spatial resolution than the atmospheric component, which is interpolated to a 2° grid (Thompson and Pollard 1997). The LSX package computes the exchange of energy and moisture between the surface and atmosphere and includes multilayer models of the soil, snow, and sea ice. The sea ice model consists of a six-layer thermodynamic model and a separate treatment for advection by surface winds and ocean currents. Because the slab ocean model does not supply prognostic ocean currents, ocean stress on the bottom of the ice is prescribed from an annual-mean climatology (Pollard and Thompson 1994). The surface albedo at each grid cell is computed as a linear combination of the background albedo and the snow albedo, weighted by the fraction of the grid cell covered with snow. Snow and ice albedos vary with their prognostic skin temperatures, decreasing linearly over a specified albedo range from −5°C to their melting temperature. A higher albedo is used for snow on glacier ice (0.70–0.95 in the visible band) than for snow on other surface types (0.55–0.90 in the visible band), which is equivalent to the albedo range assigned to bare glacier ice (0.70–0.95 in the visible band). Gridcell snow fraction is computed via a statistical relationship to the grid-cell prognostic snow depth, with the relationship weakened for grid cells with canopy vegetation. The background albedo is derived from the present-day distribution of vegetation and freshwater lakes.

We carried out a simulation of the modern climate with GENESIS to test its performance against observations in our study region. We used 1991 Intergovernmental Panel on Climate Change (IPCC) greenhouse gas levels for the modern simulation. Figure 1 shows the July 2-m surface air temperature difference between the model and the Legates and Willmott (1990) in situ–based climatology over North America.

Fig. 1.
Fig. 1.

GENESIS July surface air temperature bias over North America measured as the difference between a present-day simulation and the Legates and Willmott observational dataset. The square box refers to the region plotted in Fig. 6, and the lines of longitude refer to the transects in Fig. 7.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00218.1

GENESIS predicts July surface air temperatures that are too high by 5°C in much of northern Canada and 3°C in central Canada. This bias is thought to be due to an underestimate of summer cloudiness in the model (Thompson and Pollard 1995). A similar arctic cloud bias was reported for the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) dataset (Otieno and Bromwich 2009) and is a common shortcoming among GCMs. GENESIS also exhibits cold biases over elevated and glaciated regions (Fig. 1, i.e., the Rocky Mountains and Ellesmere Island). GENESIS underestimates (overestimates) July (January) precipitation in northern Canada by about 0.5 mm day−1 (not shown) and simulates reasonable accumulation rates over the modern day Greenland and Antarctic ice sheets (Thompson and Pollard 1997).

b. ISM

The ice sheet model (ISM) is a thermomechanical shallow ice model (Pollard and DeConto 2005) run at a horizontal resolution of 0.5° latitude by 1.0° longitude. The model uses an alternating-direction-implicit numerical scheme to solve for the vertically integrated two-dimensional mass continuity equation with a time step of 5 yr. The temperature field in the ice and adjacent bedrock is solved for at each time step for its effects on ice rheology, basal melting, and basal sliding. The geothermal heat flux is held constant at 50 W m−2. Glacial isostatic adjustment is not considered for all but one experiment, in which case it is modeled by linear relaxation toward isostatic equilibrium with a time constant of 5000 yr and the load modified by lithospheric flexure with a crustal stiffness of 1024 N m (Pollard and DeConto 2005; van den Berg et al. 2008).

The surface mass balance is computed by interpolating monthly-mean LSX surface air temperature and precipitation fields to the ice sheet model grid. Surface melting is modeled using a statistical positive degree-day (PDD) method that uses monthly mean surface air temperatures to estimate cumulative monthly PDD (Braithwaite 1984). At the beginning of each melt season, accumulated snow melts by a degree-day factor of 3.5 mm day−1 °C−1 until bare ice is exposed, which melts by a degree-day factor of 7 mm day−1 °C−1. Entrainment and refreezing of meltwater in the snowpack is parameterized by assuming that all surface melt percolates into the snow until at least 95% of the snowpack is saturated. Precipitation falls as snow if the surface air temperature is below freezing. Ice is removed (calved) once it encounters the deep ocean (grid cells greater than 750-m depth). A fixed calving water depth of 750 m ensures ice margins can traverse the relatively shallow seaways of the Canadian Archipelago and Hudson Bay (see Fig. 2) without explicitly modeling ice shelves.

Fig. 2.
Fig. 2.

ELA (solid black line) and July 0° isotherm (solid white line) simulated in the initial ice-free state and overlain on a map of the bedrock topography used in the ISM.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00218.1

Ice sheet elevations evolve between iterations with GENESIS. To account for height–mass balance feedbacks during ice sheet thickening or thinning, both temperature and precipitation fields are adjusted along fixed lapse rates. The temperature lapse rate was set to 8.5 K km−1, which is consistent with the lapse rate used in the GCM to correct for the truncated spectral topography. On ice surfaces above 2 km, the precipitation rate follows an exponential decay with elevation, decreasing by one-half for every kilometer of ice growth in order to simulate an elevation desert effect (Budd and Smith 1981).

3. Experimental design

The end of the last interglacial was triggered by the onset of very cool Northern Hemisphere summers, with an inferred maximum rate of ice advance during the insolation minimum at 116 ka (Andrews and Mahaffy 1976). This is a time when the earth’s orbit was eccentric, summer solstice (boreal) occurred near aphelion and the earth’s axial tilt was at a minimum. Here we present experiments to investigate the nonlinear process of ice sheet inception simulated by an atmospheric GCM asynchronously coupled to an ISM for 10 kyr with the 116 ka insolation minimum (Berger and Loutre 1991). Greenhouse gas concentrations were held fixed at approximate 10 kyr means obtained from ice core records (CO2: 260 ppm, CH4: 500 ppb, and N2O: 260 ppb—Petit et al. 1999; Sowers et al. 2003).

The experiments were designed to identify processes that lead to differences in the simulated ice volume and extent when the frequency of coupling between the ISM and GCM are varied. The asynchronous coupling method used here is described in Horton and Poulsen (2009); essentially, the ISM runs continuously while the GCM (i.e., the climate) is updated with ice topography and extents only periodically. The period between climate updates is referred to as the communication interval or coupling time step throughout this study. We experiment with four different communication intervals, 500, 1000, 2500, and 5000 yr, which we refer to as the f500, f1000, f2500, and f5000 experiments, respectively.

Each climate update is derived from a 25-yr-long GCM integration, of which the first 15 years are used to bring the climate into a statistical equilibrium with the updated ice sheet topography and extents. Monthly near-surface air temperature and precipitation fields are averaged over the final 10 years of the integration and passed to the ISM to compute the surface mass balance. Our use of climatological precipitation and temperature fields to force the ISM, as well as our use of slab ocean model, strongly damps interannual climate variability in GENESIS. The removal of this variability is appropriate for our methodology since the GCM and ISM communicate on decadal or longer time scales.

Geomorphic and stratigraphic evidence indicate that the Laurentide Ice Sheet nucleated in northeastern Canada (Andrews and Barry 1978; Clark et al. 1993), precisely the location of the GENESIS summer warm bias (Fig. 1). A simple way to correct for this is to subtract the monthly temperature bias from the GCM monthly temperature fields prior to passing them to the ISM. The need for bias correction represents a severe limitation of GCM–ISM studies. In GENESIS and many other GCMs, however, bias corrections are necessary to grow a realistic Laurentide Ice Sheet. The bias correction is assumed to be tied to the local land surface type (water, ice, or land) and is therefore not applied over ice or water, resulting in a reduction in mean bias as ice sheet inception proceeds. The bias correction was also not applied over Greenland, which was assumed to be ice free during the last interglacial. Similar bias corrections have been applied to a number of climate model–ice sheet studies (Vettoretti and Peltier 2003; Vizcaino et al. 2008; Ganopolski et al. 2010).

Although the GCM is a global model, the ISM was only applied over North America and Greenland in order to simulate the inception of the Laurentide and Greenland ice sheets (Fig. 2). Both Greenland and present glaciated regions in northern Canada (e.g., Ellesmere and Baffin Islands) were specified to be ice free and in isostatic equilibrium with the free surface at the start of the integration. Although the assumption of an ice-free Greenland is inconsistent with ice cores records (Landais et al. 2006), it was done to explore whether similar processes govern the inception of ice sheets on two very different landmasses.

The true topography of our study region is of course not made up of discrete 0.5° by 1.0° plateaus as depicted in Fig. 2. By employing a subgrid-scale parameterization for finescale topography, Marshall (2002) shows that the unrealistic flat topography used in ice sheet models facilitates glacial inception over a more realistic, rugged topography. Oerlemans (2002) undertook a more general treatment of the problem and showed that certain ratios of height to wavelength in topography actually promote ice sheet inception over a flat topography case. Future studies are needed to explore the role of finescale topography in glacial inception.

4. Results

The coupled model predicts extensive accumulation areas over Greenland and northeastern Canada at the beginning of the integration (Fig. 2). The envelope of these accumulation zones, or equilibrium line altitude (ELA), generally follows the 0° isotherm in the warmest summer month (Fig. 2), indicating that the intensity of the summer melt season primarily controls glacial inception in the model. A summer melt control on glacial inception is consistent with numerous modeling studies (Oglesby 1990; Vettoretti and Peltier 2003; Charbit et al. 2007; Otieno and Bromwich 2009; Otieno et al. 2011) as well as the original Milankovich hypothesis (Crowley and North 1991). The initial ELA distribution in Fig. 2 can be thought of as an initial condition for all four coupling experiments.

a. Ice volume and area evolution

The four coupling experiments show significant differences in predicted ice volume and area over the duration of the experiments (Fig. 3). At the end of 10 kyr, the experiments produce Canadian ice volumes in the range from 3 to 6 (×106) km3, which corresponds to an estimated sea level drop of 6–12 m (corrected for isostatic loading of the oceans on the lithosphere). The f500 experiment leads to ice volumes over Canada that are nearly double those of the f5000 experiment and three times the ice volume without any coupling (not shown). In contrast, ice volumes for the Greenland experiments are relatively insensitive to the coupling frequency, with all four coupling experiments producing approximately 4 × 106 km3 of ice or 8 m of sea level lowering at the end of 10 kyr.

Fig. 3.
Fig. 3.

Time series of ice volume and ice area in (a),(b) Canada and (c),(d) Greenland for all coupling experiments. Equivalent sea level (right axis) is corrected for isostatic loading on the lithosphere. Ice area is often referred to as accumulation area in the text because they are approximately equal during the first 10 kyr, consistent with theory (Weertman 1964). Note the change in scale of the time axis at year 10 000.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00218.1

The growth in Canadian ice volume during the first 10 kyr is primarily controlled by abrupt increases in accumulation area (Figs. 3a,b). This is most easily detected in the ice volume curve from the f5000 experiment, where breaks in the slope occur when there are abrupt increases in accumulation area. The ice volume curve for the f500 experiment looks continuous, but the time derivative of ice volume shows discrete steps in the growth rate in response to increases in accumulation area (not shown). For Greenland, gains in accumulation area from such jumps are smaller and similar in magnitude to gains by ice flow, so the communication interval is less important to simulated ice volume at the end of 10 kyr. This apparent lack of sensitivity to the coupling time step is simply because much of Greenland lies within an accumulation zone at the beginning of the integration (Fig. 2) and, as a result, large increases in accumulation area are not possible.

The accumulation area increases in response to GCM climate updates. These gains are initially large, but dampen with each subsequent update with only marginal gains in area after the fourth iteration (Fig. 3b). This accumulation history suggests that the process limiting growth becomes more effective as the ice sheet grows larger. Interestingly, the shorter coupling time step leads to a greater accumulation area and total ice volume over Canada (Figs. 3a,b). This difference is due to how the ice sheet evolves under different coupling frequencies. With a short coupling time step, the ice sheet undergoes less accumulation before the GCM climate is updated. After the climate update, the ice sheet grows outward into regions that are now exposed to perennially below freezing temperatures. Consequently, a short coupling frequency produces large but low ice sheets. With a longer coupling time step, the ice sheet has more time to grow upward between climate updates, leading to smaller but higher ice sheets. As discussed in the next section, the height of the ice sheet ultimately acts to stunt further expansion.

To gain insight into the role of the coupling frequency in simulating ice sheets over longer time periods, the ISM was run continuously for an additional 30 kyr without updating the climate (i.e., uncoupled) for the f500 and f5000 experiments, at which point one climate update was made and the experiments were integrated an additional 10 kyr. In both the f500 and f5000 experiments, the Greenland Ice Sheet reaches steady state by 20 kyr, whereas the Laurentide Ice Sheet is still equilibrating after 50 kyr (Figs. 3a,c). The difference in Canadian ice volume between the f500 and f5000 experiments shrinks from 3 × 106 km3 at 10 kyr to 2 × 106 km3 at 40 kyr, indicating that the evolution of Canadian ice volume over 40 kyr is still quite sensitive to the number of coupling iterations in the first 10 kyr. The final climate update at 40 kyr does not cause an abrupt increase in accumulation area for the f500 experiment but does lead to a slightly greater ice volume growth rate for an additional 5 kyr. In contrast, the 40-kyr climate update in the f5000 experiment leads to a small stepwise gain in accumulation area, resulting in a greater ice volume growth rate for the remaining 10 kyr.

b. Summer climate evolution

Due to the dependence of glacial inception on the summer climate in the model, the stepwise increases in accumulation area, as well as their tendency to dampen with each climate update, can be understood by analyzing climate statistics of the peak summer month. This month is referred to as July here for simplicity, recognizing that the timing of peak summer insolation was different 116 ka owing to the orbital configuration (Joussaume and Braconnot 1997).

Figure 4a shows the change in the July surface air temperature for the f500 experiment just after the first coupling time step (year 500) compared to the initial ice-free state. The year 500 temperature field represents the climate conditions that produce the first abrupt increase in ice extent. The higher albedo of the nucleating ice centers in northern Canada result in local as well as nonlocal temperature reductions, extending as far as 2000 km from the ice. In effect, the local albedo-induced cooling is spread out through horizontal dampening processes in the model, which lowers the ELA. The ISM responds by a stepwise increase in ice area at year 505 so that during the next climate update (year 1000) the albedo increase over Canada is even greater, and another increase in ice area occurs at year 1005. This positive feedback on ice sheet growth is the coupled model’s expression of the SICI.

Fig. 4.
Fig. 4.

Difference in July surface air temperature between various times throughout the f500 experiment and the initial ice-free state (CNTL). Areas covered by ice throughout the experiment are masked out.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00218.1

Horizontal dampening processes become less efficient as the ice sheet grows since the accumulation area jumps are reduced with each subsequent climate update. Figure 4b shows the change in the July surface air temperature for the f500 experiment just after the final coupling time step (year 9500) compared to the initial ice-free state. Surprisingly, the overall effect of the mature Laurentide Ice Sheet is to warm the adjacent land areas to the south along a band stretching from northwestern Canada to the eastern United States. The magnitude of the July surface air temperature anomalies increase as the ice sheet continues to grow (Fig. 4c).

To understand whether warming of the Laurentide Ice Sheet margin increases with ice area or ice elevation, we repeat the climate update at year 40 000 but impose an ice sheet with the same extent with no topography (i.e., a flat ice sheet). In this case, the flat ice sheet causes extensive cooling over adjacent land areas (Fig. 4d), which resembles the temperature anomaly at year 500 in the f500 experiment (Fig. 4a). A similar result was obtained in the flat ice sheet experiment of Felzer et al. (1996) using a coarser-resolution GCM. The cooling influence of flat ice sheets indicates that the development of ice sheet topography opposes horizontal dampening processes in the GCM and warms the margin of the growing Laurentide Ice Sheet.

Warming along the margin of the Laurentide Ice Sheet occurs through its interaction with the atmospheric circulation. Glacial anticyclones develop over the Laurentide and Greenland ice sheets early in the experiments and intensify as ice elevations grow. Figures 5a,b shows the change in July sea level pressure and low-level winds for years 9500 and 40 000 relative to the control in the f500 experiment. Regions of Hudson Strait and Alaska experience strong southerly flow up ice sheet margins (Figs. 5a,b), increasing July precipitation by up to 2 and 4 mm day−1 for years 9500 and 40 000, respectively (not shown). A mature stationary wave pattern, with high pressure and anticyclonic flow situated over the Laurentide and Greenland ice sheets, exists at both intervals. Theoretically, we would expect the stationary anticyclones to induce zonal asymmetry in the temperature field, with warming upstream of the high pressure and cooling downstream. The surface air temperature anomaly pattern is consistent with this expectation (Figs. 4b,d) as are changes in the July vertically averaged meridional flux of sensible heat (Figs. 5c,d). Interestingly, the downstream flux of cold air occurs predominantly offshore in the Labrador and North Atlantic region, and therefore only the upstream flux of warm air noticeably affects the mass balance of the Laurentide Ice Sheet (however, the accelerated ice growth at year 40 000 in the f500 experiment is due to downstream cooling over a small unglaciated region on the eastern coast of Quebec). The net effect of this stationary wave feedback is therefore to oppose southward and westward expansion of the Laurentide Ice Sheet and serves as a formidable obstacle to coalescence with the Cordilleran Ice Sheet (Fig. 6). This result is consistent with another GENESIS–ISM study (Charbit et al. 2007), in which the two ice sheets did not coalesce under Last Glacial Maximum boundary conditions.

Fig. 5.
Fig. 5.

(a),(b) Departure of July sea level pressure and July surface winds from the initial ice-free state (CNTL) at various times throughout the f500 experiment and (c),(d) difference in July vertically integrated northward transport of sensible heat from the initial ice-free state (CNTL) at various time throughout the f500 experiment. The thick black line is zero contour and the solid (dashed) lines are positive (negative) values, contour interval 100 K m s−1.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00218.1

Fig. 6.
Fig. 6.

Scatterplot of July surface air temperature relative to the ice-free run for all climate updates averaged over a land region between the Laurentide and Cordilleran ice sheets (see Fig. 1) against mean height of the Laurentide Ice Sheet lying under anticyclonic flow. As the Laurentide Ice Sheet grows in height, the July summer temperatures increase.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00218.1

The sequence of feedback processes is illustrated by analyzing years 1000, 3000, and 5000 of the f500 experiment since the stepwise gains in accumulation area become progressively damped over this time period (Fig. 3b). Figure 7 shows the change in July surface air temperature in the latitude–height plane relative to the initial ice-free state for transects through western, central, and eastern Canada (locations shown in Fig. 1), for the three time slices. The transition from a cooling to a warming influence on the ice-free land is evident by following the southward extent of the 0° isotherm. The thin Laurentide Ice Sheet at year 1000 is characterized by a relatively shallow cooling influence that extends well south of the ice sheet, with warmer air overlying the ice in the middle troposphere. This warm air is consistent with an upward and poleward heat flux across the ice margin as a result of the horizontal dampening process. In contrast, the cooling influence of the ice sheets at year 5000 extends throughout the entire depth of the troposphere, acting as a barrier to the pocket of warm air that is now located south of the ice margin and closer to the land surface. This represents the blocking effect of the maturing glacial anticyclone and results in a retreat of the 0° isotherm to the ice margin. Further growth of the ice sheet intensifies the pattern seen in year 5000 by intensifying heat transport to the ice margin through southerly flow.

Fig. 7.
Fig. 7.

Difference in July atmospheric temperature for years (left) 1000, (right) 3000, and (right) 5000 in the high-frequency coupling experiment and the initial ice-free state in the latitude–height plane for (top) western, (middle) central, and (bottom) eastern Canada. See Fig. 1 for exact locations. Thick black line is the zero contour and solid (dashed) lines indicate positive (negative) values, contour interval 0.5 K.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00218.1

The dependence of the stationary wave feedback on ice elevation has implications for the role of glacial isostasy in ice sheet growth. Although isostasy acts to keep ice elevations lower than they would otherwise be, there is considerable debate whether this acts to increase or decrease the surface mass balance relative to a case with no isostatic adjustment (Crucifix et al. 2001; van den Berg et al. 2008). Our results suggest that lower ice elevations will reduce the effect of the negative stationary wave feedback, increasing the surface mass balance relative to the no-isostasy case. We performed an experiment with the isostasy model turned on to test this idea. Our results show that, for a 500-yr communication interval, glacial isostasy acts as a small positive feedback on ice growth, contributing 0.5 × 106 km3 (1 m sea level equivalent) to the total simulated ice volume (Canadian and Greenland ice) at the end of 10 kyr.

5. Discussion

An ice volume growth rate of 50 m sea level equivalent in 10 kyr remains a daunting task for GCM studies, even through asynchronously coupling an atmospheric GCM to an ISM. Our total sea level lowering after 10 kyr, assuming a constant 116-ka orbit, an initially ice-free Greenland, and a rather large bias correction, is 20 m. However, the f500 experiment produces a Laurentide ice volume that is an order of magnitude greater than was simulated in a previous study (Pollard and Thompson 1997) using the same models and with a very similar experimental design (including a temperature bias correction), but without asynchronous coupling (forced the ISM offline for 10 kyr with the initial ice-free GCM climate). Our simulated ice volume is larger than that simulated in Pollard and Thompson, mainly because of the asynchronous coupling scheme, which results in a greater lowering of the ELA because of the SICI feedback.

The SICI feedback is triggered when the ISM prescribes ice-covered grid cells to the GCM, which increases the albedo and therefore the magnitude of cooling over snow-covered grid cells. Ice-covered grid cells increase the albedo of snow-covered grid cells in two ways: by increasing the albedo of snow from a range of 0.55–0.90 (over land) to a range of 0.70–0.95 (over ice) and by changing the background albedo of the grid cell to ice (important for grid cells only partially covered with snow).

That the SICI arises from an ice instability, as opposed to a snow instability, is consistent with another study showing that natural variability of the snow line (in space and in time) results in a damped SICI response in a GCM (Lee and North 1995). Following this line of reasoning, ice caps are more prone to instability because their land-terminating margins do not experience the same degree of variability as a seasonal snow line. However, a previous study using an earlier version of GENESIS to investigate the Carboniferous ice age identified a snow-triggered SICI response (Crowley et al. 1994). The carboniferous experiment differs from ours in that perennial snow formed over a pole-centered continent, Gondwanaland, whereas in our study the Laurentide Ice Sheet forms on a warmer, midlatitude continent. Therefore, ice-covered grid cells are not a requirement for the SICI to occur, but their inclusion moves the bifurcation point such that a smaller change in external forcing triggers the SICI.

Previous studies using coupled atmosphere–ocean GCMs have reported that the expansion of Arctic sea ice favors perennial snowfields in northeastern Canada (Khodri et al. 2005; Otieno et al. 2011). Khodri et al. (2005) find that the seasonal expansion of sea ice due to favorable precessional forcing 115 ka increases the surface albedo over northern Canada, causing cooling, enhanced moisture convergence from the subtropical Atlantic, and ultimately increased snowfall. Otieno et al. (2011) indicate that sea ice expansion through the Bering Strait causes increased cyclonic activity in the North Pacific, favoring the development of anticyclonic flow and cooling downstream in northeastern Canada. We do not find a substantial role for sea ice in our experiments. The sea ice extent increases only marginally around Canada and the North Pacific throughout our experiments (not shown) and these increases do not coincide with the abrupt gains in ice sheet area occurring in the first few climate updates (Fig. 3). It is possible that the inclusion of a dynamic ocean model may lead to a larger role for sea ice in Laurentide inception in our coupled model. Alternatively, the addition of an ice sheet model in the AOGCM studies might result in a SICI mechanism of Laurentide inception as well.

The strength of the SICI in our experiments decreases when the communication interval is lengthened for two reasons. The first reason is that long communication intervals result in fewer climate updates and thus fewer opportunities for ice area expansion through the SICI. The less obvious, second reason is that, since the stationary wave feedback strengthens in response to higher ice topography, a long communication interval results in a larger stationary wave response during the first few climate updates compared to a small communication interval. The SICI feedback is opposed by the stationary wave response, so the SICI feedback is reduced when long communication intervals are used.

The inverse relationship between simulated ice volume and the communication interval suggests that using a communication interval shorter than 500 yr may result in larger ice volumes that are closer to those observed in the geologic record. Because the SICI response requires ice-covered grid cells, an appropriate ISM–GCM communication interval should be the length of time it takes a perennial snowfield to have the reflective properties of snow over ice in the GCM. This length of time is probably less than the time it takes a snowfield to convert to an ice cap since the albedo over a few-meter-thick snowfield (e.g., less than 100 years old) would no longer have the albedo properties of snow over land. The marginal effect of climate updates on ice volume once the SICI is saturated warrants the use of longer communication intervals between the GCM and ISM. We therefore propose an adaptive asynchronous coupling scheme, similar to that used by Ridley et al. (2009), in which a short communication interval is lengthened after the SICI feedback is exhausted.

The stationary wave feedback is negative in our experiments simply because of the geographic location of the nucleating Laurentide Ice Sheet. If an ice sheet nucleated along the west coast of a continent, the stationary wave feedback may have an opposite sign since southerly air induced by the glacial anticyclone would be upwind and offshore, whereas the northerly branch would be downwind and onshore. Because eastern Canada is cooler than its western counterpart [due to stationary waves imposed by the Rocky Mountains, Seagar et al. (2002)], the Laurentide Ice Sheet was initiated out of northeastern Canada (Andrews and Barry 1978; Clark et al. 1993) and the resulting feedback is negative. Further, the orientation of the glacial anticyclone causes the Laurentide Ice Sheet to have a right-triangular geometry with its diagonal margin defined by the incursion of warm air from the south (Figs. 4b,c). A triangular-shaped Laurentide Ice Sheet is supported by the diagonal alignment of the largest glacially eroded overdeepenings in Canada (e.g., Great Bear Lake, Great Slave Lake, and the Great Lakes; see land mask in Fig. 2), indicating this region is the preferred location of the ice margin since the onset of Pleistocene glaciations.

6. Conclusions

The rapid nucleation and expansion of the Laurentide Ice Sheet 116 ka has been attributed to the small ice cap instability (SICI). Although energy balance models (EBMs) and earth models of intermediate complexity (EMICs) have demonstrated this instability, GCMs have not, casting some doubt on the fidelity of these simpler models. In this study, we demonstrate SICI-like behavior in a GCM asynchronously coupled to an ice sheet model (ISM). With a coupling interval of 500 yr, the GCM–ISM simulates a combined Canadian and Greenland ice volume of 20 m sea level equivalent in 10 kyr. The simulated ice volume is reduced to 14 m sea level equivalent when the coupling interval is increased to 5000 yr. The reduction in ice volume with an increase in coupling interval is attributed to an enhanced negative stationary wave feedback under weak SICI behavior. The SICI causes cooling in front of the ice margin, promoting perennial snowpack and ice sheet expansion over a large area. When the SICI is weak owing to infrequent GCM–ISM coupling, the ice sheet grows upward, strengthening anticyclonic circulation that transports heat and promotes above freezing summer temperatures along the southwestern margin of the Laurentide Ice Sheet.

Our results provide an explanation for the rapid onset of continental glaciation 116 ka through the SICI and demonstrate the importance of negative stationary wave feedbacks on the evolution of the Laurentide Ice Sheet. Furthermore, our results support the use of an adaptive asynchronous coupling scheme to more accurately capture the strength of these feedbacks, potentially leading to greater simulated ice volume as suggested by the geological record.

Acknowledgments

We thank D. Pollard for providing technical advice in using his ice-sheet model. We are also grateful for the constructive comments of three reviewers. This work was supported by NSF Grant OCE 0902258.

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